TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND … · TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN The design values in the equation may be calculated

–410–

TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN

(3)PerformanceverificationofSRCMembers

① Thesteelandreinforcedconcrete(SRC)membersshallbedesignedagainsttheflexuralmomentandshearingforce,bytakingfullaccountofthestructuralcharacteristicsduetodifferencesinthestructuraltypeofthesteelframe.

② SRCmemberscannormallybeclassifiedasfollows,dependingonthestructuraltypeofsteelframes:

(a) Full-webtype

(b)Trusswebtype

③ Fortheflexuralmoment,thesectionstresscanbecalculatedasareinforcedconcretememberbyconvertingsteelframestoequivalentreinforcements.Whenthefixingofsteelframeendswithconcreteisinsufficientinfull-webtype,itshouldbecalculatedasacompositeoftheindependentsteelframememberandthereinforcedconcretemember.

④ Forshearingforce,ifthewebisoftrusstype,theshearstresscanbecalculatedasareinforcedconcretebyconvertingsteelframestoequivalentreinforcements.Ifitisoffull-webtype,steelframesthemselvescanresistagainsttheshearingforce,andtheycanbedulyconsideredindesign.

(4)PerformanceVerificationofPartitionWalls

Becausepartitionwallsfunctionasabearingsideoftheouterwallsandbottomslab,inperformanceverification,stabilityofthecrosssectionofthepartitionwallshouldbesecuredagainstthesectionalforcescalculatedbasedontheactionsonthesebearingsides.

(5)PerformanceVerificationofCornersandJoints

① Cornersandjointsshallbedesignedtosmoothlyandfirmlytransmitsectionforces,andtobeeasilyfabricatedandexecuted.

② Tosecuresufficientstrengthatcornersandjoints,itisdesirabletofirmlyconnectthesteelmaterialsonthetensile side to thoseof thecompressiveside. It isalsodesirable toprovideshear reinforcedsteelmaterials(haunches)againstconcretetensilestressoftheinsideofjoints.

(6)PerformanceVerificationforFatigueFailure

① Hybridcaissonsusealargenumberofweldedjointsforconnectingsteelplates,andattachingshearconnectorsandshearresistancesteel.Therefore,wherethemembersarefrequentlysubjecttorepeatedload,thefatiguestrengthinweldedpartsshouldbeexamined.

② In coastal revetments and quaywalls, the influence of repeated actions is small. However, in performanceverificationsofbreakwaters,whenthestressonmembersduetowavesasarepeatedactionchangessignificantly,examinationforfatiguefailureofthecaissonisneeded.

1.6.5 Corrosion Control

(1)Corrosioncontrolofhybridcaissonsshallbesetappropriatelyconsideringtheperformancerequirements,levelofmaintenancecontrol,constructionconditions,andotherrelevantfactors.

(2)Themaincauseofdeteriorationofhybridmembersiscorrosionofthesteelmaterials.Becausetherearecasesinwhichcorrosionofthesteelmaterialsmayresultindevelopingcracksoftheconcrete,appropriatecorrosionpreventionmeasuresshouldbetakenforsteelplatesinordertoimprovethedurabilityofthehybridmembers.Thedeteriorationcharacteristicsoftheconcreteitselfshouldbeconsideredtobethesameasthatofconventionalreinforcedconcrete.

(3)Steelmaterialsusedontheoutsideofhybridcaissonsaregenerallycoveredwithconcreteorasphaltmats.Theinsideofacaissonisisolatedfromtheexternalatmospherebymeansofconcretelids.Itisalsoincontactwithfillingsand inastaticstateandwithresidualseawater. Thus,whendesigninghybridcaissons,directcontactbetweenthesteelplatesofmembersandthemarineenvironmentisgenerallyavoided.Forcorrosioncontrol,itisusualtosetsteelplateontheinsideandconcreteontheoutsidesoastoavoiddirectcontactofsteelplatewithfreshseawater.Ifsteelplatesareindirectcontactwithseawater,corrosioncontrolshouldbeappliedsuchascoatingmethodstosplashzoneortidalzoneandcathodicprotectionmethodsinseawater.

PART III FACILITIES, CHAPTER 2 ITEMS COMMON TO FACILITIES SUBJECT TO TECHNICAL STANDARDS

–411–

1.7 Armor Stones and BlocksPublic NoticePerformance Criteria of Armor Stones and Blocks

Article 28 Theperformancecriteriaofrubblestonesandconcreteblocksarmoringastructureexposedtotheactionsofwavesandwatercurrentsaswellasarmorstonesandarmorblocksofthefoundationmoundshallbesuchthattheriskofexceedingtheallowabledegreeofdamageunderthevariableactionsituation,inwhichthedominantactionsarevariablewavesandwatercurrents,isequaltoorlessthanthethresholdlevel.

[Commentary]

(1)PerformanceCriteriaofArmorStonesandBlocksThesettingsoftheperformancecriteriaanddesignsituations,excludingaccidentalsituations,forarmorstonesandblocksshallbeasshownintheAttached Table 14.

Attached Table 14 Settings for Performance Criteria and Design Situations (excluding accidental situations) for Armor Stones and Blocks

MinisterialOrdinance PublicNotice

Performancerequirements

Designsituation

Verificationitem Indexofstandardlimitvalue

Article

Paragraph

Item

Article

Paragraph

Item Situation Dominatingaction

Non-dominatingaction

7 1 – 28 1 – Serviceability Variable Variablewaves Selfweight,waterpressure

Extentofdamage Limitvalueofdamagerate,degreeofdamage,ordeformationlevel

①ExtentofdamageTheindexeswhichexpresstheextentofdamageofarmorstonesandblocksforthevariablesituationsinwhichthedominatingactionsarevariablewavesandwatercurrentsarethedamagerate,thedegreeofdamage,andthedeformationlevel. In theperformanceverificationofarmor stonesandblocks, the indexes including thedegreeofdamageandthelimitvaluethereofshallbesetappropriatelyconsideringthedesignworkinglifeoftheobjectivefacilities,theconstructionworkconditions,thetimeandcostnecessaryforrestoration,andtheconditionsofwavesandwatercurrents,etc.

[Technical Note]

1.7.1 Required Mass of Armor Stones and Blocks on Slope24),25)

(1)GeneralThe armor units for the slopes and a sloping breakwaters are placed to protect the rubble stones inside; it isnecessarytoensurethatanarmorunithasamasssufficienttobestablesothatitdoesnotscatteritself.Thisstablemass,requiredmass,cangenerallybeobtainedbyhydraulicmodeltestsorcalculationsusingappropriateequations.

(2)BasicEquationforCalculationofRequiredMassWhencalculatingtherequiredmassofrubblestonesandconcreteblockscoveringtheslopeofaslopingstructurewhichisaffectedbywaveforces,Hudson’sformulawiththestabilitynumberNS,whichisshowninthefollowingequation,maybeused.26)Inthisequation,thesymbolγisapartialfactorforitssubscript,andthesubscriptskanddshowthecharacteristicvalueanddesignvalue,respectively.ForthepartialsafetyfactorsγNS andγH intheequation,1.0maybeused.

(1.7.1)where

M :requiredmassofrubblestonesorconcreteblocks(t) ρr :densityofrubblestonesorconcreteblocks(t/m3) H :waveheightusedinstabilitycalculation(m) NS :stabilitynumberdeterminedprimarilybytheshape,slope,damagerateofthearmor,etc. Sr :specificgravityofrubblestonesorconcreteblocksrelativetowater

–412–


Thedesignvaluesintheequationmaybecalculatedusingthefollowingequations.

(3)DesignWaveHeightHUsedinthePerformanceVerificationHudson’sformulawasproposedbasedontheresultsofexperiments thatusedregularwaves. Whenapplyingit totheactionofactualwaveswhicharerandom,thereisthusaproblemofwhichdefinitionofwaveheightsshallbeused.However,withstructuresthataremadeofrubblestonesorconcreteblocks,thereisatendencyfordamagetooccurnotwhenonesinglewavehavingthemaximumheightH amongarandomwavetrainattacksthearmorunits,butratherfordamagetoprogressgraduallyunderthecontinuousactionofwavesofvariousheights.Consideringthisfactandpastexperiences,ithasbeendecidedtomakeitstandardtousethesignificantwaveheightofincidentwavesattheplacewheretheslopeislocatedasthewaveheightH inequation (1.7.1),becausethesignificantwaveheightisrepresentativeoftheoverallscaleofarandomwavetrain.Consequently,itisalsostandardtousethesignificantwaveheightwhenusingthegeneralizedHudson’sformula.Notehoweverthatforplaceswherethewaterdepthislessthanonehalfoftheequivalentdeepwaterwaveheight,thesignificantwaveheightatthewaterdepthequaltoonehalfoftheequivalentdeepwaterwaveheightshouldbeused.

(4)ParametersAffectingtheStabilityNumberNSAsshowninequation (1.7.1),therequiredmassofarmorstonesorconcreteblocksvarieswiththewaveheightandthedensityofthearmorunits,andalsothestabilitynumberNS.TheNS valueisacoefficientthatrepresentstheeffectsofthecharacteristicsofstructure,thoseofarmorunits,wavecharacteristicsandotherfactorsonthestability.ThemainfactorsthatinfluencetheNS valueareasfollows.

① Characteristicsofthestructure

(a) Type of structure; sloping breakwater, breakwater covered with wave-dissipating concrete blocks, andcompositebreakwater,etc.

(b)Gradientofthearmoredslope

(c) Positionofarmorunits;breakwaterhead,breakwatertrunk,positionrelativetostillwaterlevel,frontfaceandtopofslope,backface,andberm,etc.

(d)Crownheightandwidth,andshapeofsuperstructure

(e) Innerlayer;coefficientofpermeability,thickness,anddegreeofsurfaceroughness

② Characteristicsofthearmorunits

(a) Shapeofarmorunits(shapeofarmorstonesorconcreteblocks;forarmorstones,theirdiameterdistribution)

(b)Placementofarmorunits;numberoflayers,andregularlayingorrandomplacement,etc.

(c) Strengthofarmormaterial

③Wavecharacteristics

(a) Numberofwavesactingonarmorlayers

(b)Wavesteepness

(c) Formofseabed(seabedslope,whereaboutofreef,etc.)

(d)Ratioofwaveheighttowaterdepthasindicesofnon-breakingorbreakingwavecondition,breakertype,etc.

(e)Wavedirection,wavespectrum,andwavegroupcharacteristics

④ Extentofdamage(damageratio,deformationlevel,relativedamagelevel)Consequently, theNS valueusedintheperformanceverificationmustbedeterminedappropriatelybasedonhydraulicmodelexperimentsinlinewiththerespectivedesignconditions.Bycomparingtheresultsofregularwavesexperimentswiththoseofrandomwaveexperiments,27)itwasfoundthattheratiooftheheightofregularwavestothesignificantheightofrandomwavesthatgavethesamedamageratio,withintheerrorof10%,variedintherangeof1.0to2.0,dependingontheconditions.Inotherwords,therewasatendencyfortherandomwaveactiontobemoredestructivethantheactionofregularwaves.Itisthusbettertoemployrandomwavesinexperiments.


–413–

(5)StabilityNumberNS andKDValueIn1959,Hudsonpublishedtheso-calledHudson’sformula,26)replacingthepreviousIribarren-Hudson’sformula.Hudsondevelopedequation (1.7.1)byhimselfusingKD cotαinsteadofNS.

(1.7.3)

where α :angleoftheslopefromthehorizontalline(°) KD :constantdeterminedprimarilybytheshapeofthearmorunitsandthedamageratio

TheHudson’sformulawasbasedontheresultsofawiderangeofmodelexperimentsandhasproveditselfwellinusagein-site.ThisformulausingtheKD valuehasthusbeenusedinthecalculationoftherequiredmassofarmorunitsonaslope. However,theHudson’sformulathatusesthestabilitynumberinequation (1.7.1)hasbeenusedforquiteawhileforcalculatingtherequiredmassofarmorunitsonthefoundationmoundofacompositebreakwaterasdiscussedin1.7.2 Required Mass of Armor Stones and Blocks in Composite Breakwater Foundation Mound against Waves,andisalsousedforthearmorunitsofotherstructuressuchassubmergedbreakwaters.ItisthusnowmorecommonlyusedthantheoldformulawiththeKD value. ThestabilitynumberNS canbederivedfromtheKD valueandtheangleαoftheslopefromthehorizontallinebyusingequation (1.7.3)ThereisnoproblemwiththisprocessiftheKD valueisanestablishedoneandtheslopeangleiswithinarangeofnormaldesign.However,mostoftheKD valuesobtaineduptothepresenttimehavenotsufficientlyincorporatedvariousfactorslikethecharacteristicsofthestructureandthewaves.Thus,thismethodofdetermining the stabilitynumberNS from theKD value cannotbeguaranteed toobtain economicaldesignalways.Inordertocalculatemorereasonablevaluesfortherequiredmass,itisthuspreferabletousetheresultsofexperimentsmatchedtotheconditionsinquestion,orelsetousecalculationformulas,calculationdiagrams,thatincludethevariousrelevantfactorsasdescribedbelow.

(6)VanderMeer’sFormulaforArmorStonesIn1987,vanderMeercarriedoutsystematicexperimentsconcerningthearmorstonesontheslopeofaslopingbreakwaterwithahighcrown.Heproposedthefollowingcalculationformulaforthestabilitynumber,whichcan consider not only the slopegradient, but also thewave steepness, thenumberofwaves, and thedamagelevel.28)NotehoweverthatthefollowingequationshavebeenslightlyalteredincomparisonwithvanderMeer’soriginaloneinordertomakecalculationseasier.Forexample,thewaveheightH2%forwhichtheprobabilityofexceedanceis2%hasbeenreplacedbyH1/20.

(1.7.4)

(1.7.5)

(1.7.6)

where Nsp :stabilitynumberforplungingbreakers Nssr :stabilitynumberforsurgingbreaker Ir :iribarrennumber(tanα/Som0.5)),alsocalledthesurfsimilarityparameter Som :wavesteepness(H1/3/L0) L0 :deepwaterwavelength(L0=gT1/32/2π,g=9.81m/s2) T1/3 :significantwaveperiod CH :breakingeffectcoefficient{=1.4/(H1/20/H1/3)},(=1.0innon-breakingzone) H1/3 :significantwaveheight H1/20 :highestone-twentiethwaveheight,seeFig. 1.7.1 α :angleofslopefromthehorizontalsurface(°) Dn50 :nominaldiameterofarmorstone(=(M50/ρr)1/3) M50 :50%valueofthemassdistributioncurveofanarmorstonenamelyrequiredmassofanarmor

stone P :permeabilityindexoftheinnerlayer,seeFig. 1.7.2 S :deformationlevel(S=A/Dn502),seeTable 1.7.1 A :erosionareaofcrosssection,seeFig. 1.7.3 N :numberofactingwaves

–414–


Thewave heightH1/20 inFig. 1.7.1 is for a point at a distance 5H1/3 from the breakwater, andH0’ is theequivalentdeepwaterwaveheight.ThedeformationlevelS isanindexthatrepresentstheamountofdeformationofthearmorstones,anditisakindofdamageratio.ItisdefinedastheresultoftheareaA erodedbywaves,seeFig. 1.7.3,beingdividedbythesquareofthenominaldiameterDn50ofthearmorstones.AsshowninTable 1.7.1,threestagesaredefinedwithregardtothedeformationlevelofthearmorstones : initial damage,intermediatedamage,andfailure.Withthestandarddesign,itiscommontousethedeformationlevelforinitialdamageforN =1000waves.However,incasewhereacertainamountofdeformationispermitted,usageofthevalueforintermediatedamagemayalsobeenvisaged.

1.4

1.3

1.3

1.2

1.2

1.3

1.2

1.4

1.4

0 0.5 1 1.5 2 2.5 3 3.5 4

H1/20/H1/3

h/H0'

H0'/L0

0.08 0.04 0.02 0.010.0050.002

Sea Bottom slope 1/100Sea Bottom slope 1/100



H0′: Equivalent deepwaterwave heightH0′: Equivalent deepwaterwave height

Fig. 1.7.1 Ratio of H1/20 to H1/3 (H1/20 Values are at a Distance 5H1/3 from the Breakwater)

P=0.1 P=0.4

P=0.5 P=0.6

(a) (b)

(c) (d)

Dn50A = Nominal diameter of armor stones

Dn50C = Nominal diameter of core materialDn50F = Nominal diameter of filter material

2Dn50A

2Dn50A

1.5Dn50A

2Dn50

0.5Dn50A

Dn50A/Dn50F =4.5

Dn50A/Dn50C =3.2

Dn50A/Dn50F =2Dn50F/Dn50C =4

Armor layer

Armor layer

Armor layer

Armor layer

Core

Filter layerFilter layerImpermeable

layer

No filter, no core

Fig. 1.7.2 Permeability Index P


–415–

S.W.L

A (Area of eroded part)

Fig. 1.7.3 Erosion Area A

Table 1.7.1 Deformation Level S for Each Failure Stage for a Two-layered Armor

Slope Initialdamage Intermediatedamage Failure1:1.51:21:31:41:6

22233

3–54–66–98–128–12

88121717

(7)FormulationforCalculatingStabilityNumberforArmorBlocksincludingWaveCharacteristicsVanderMeerhascarriedoutmodelexperimentsonseveralkindsofprecastconcreteblocks,andproposedtheformulasforcalculatingthestabilitynumberNS.29)Inaddition,otherpeoplehavealsoconductedresearchintoestablishingcalculationformulasforprecastconcreteblocks.Forexample,BurcharthandLiu30)haveproposedacalculationformula.However,itshouldbenotedthatthesearebasedontheresultsofexperimentsforaslopingbreakwaterwithahighcrown.Takahashietal.31)showedaperformanceverificationmethodofthestabilityagainstwaveactionforarmorstonesofaslopingbreakwaterusingVanderMeer’sformulaastheverificationformula,andproposedtheperformancematrixusedforperformanceverification.

(8)FormulasforCalculatingStabilityNumberforConcreteBlocksofBreakwaterCoveredwithWave-dissipatingBlocksThewave-dissipatingconcreteblockpartsofabreakwatercoveredwithwave-dissipatingblocksmayhavevariouscross-sections.Inparticular,whenallthefrontfaceofanuprightwalliscoveredbywave-dissipatingconcreteblocks,thestabilityishigherthanthatofarmorconcreteblocksofanordinaryslopingbreakwaterbecausethepermeabilityishigh.InJapan,muchresearchhasbeencarriedoutonthestabilityofbreakwaterscoveredwithwave-dissipatingconcreteblocks.Forexample,Tanimotoetal.32),Kajimaetal.33),andHanzawaetal.34)havecarriedoutsystematicresearchonthestabilityofwave-dissipatingconcreteblocks. Inaddition,Takahashietal.35)haveproposedthefollowingequationforwave-dissipatingconcreteblocksthatarerandomlyplacedinallthefrontfaceofanuprightwall.

(1.7.7)where

N0 :degreeofdamage,akindofdamageratethatrepresentstheextentofdamage:itisdefinedasthenumberofconcreteblocksthathavemovedwithinawidthDn inthedirectionofthebreakwateralignment,whereDn isthenominaldiameteroftheconcreteblocks:Dn=(M/ρr)1/3,whereM isthemassofaconcreteblock

CH :breakingeffectcoefficient;CH=1.4/(H1/20/H1/3),innon-breakingzoneCH =1. a,b :coefficientsthatdependontheshapeoftheconcreteblocksandtheslopeangle.Withdeformed

shapeblockshavingaKDvalueof8.3,itmaybeassumedthata =2.32andb =1.33,ifcotα=4/3,anda =2.32andb =1.42,ifcotα=1.5.

Takahashi et al.35)have further presented amethod for calculating the cumulative degree of damage, theexpecteddegreeofdamage,overtheservicelifetime.Inthefuture,reliabilitydesignmethodsthatconsidertheexpecteddegreeofdamageisimportantasthemoreadvanceddesignmethod.Intheregionwherewavebreakingdoesnotoccur,ifthenumberofwavesis1000andthedegreeofdamageN0is0.3,thedesignmassascalculatedusingthemethodofTakahashietal.ismore-or-lessthesameasthatcalculatedusingtheexistingKD value.ThevalueofN0=0.3correspondstotheconventionallyuseddamagerateof1%.

(9) IncreaseofMassinBreakwaterHeadWavesattacktheheadofabreakwaterfromvariousdirections,andthereisagreaterriskofthearmorunitsonthe

–416–


topoftheslopefallingtotherearratherthanthefront.Therefore,rubblestonesorconcreteblockswhicharetobeusedattheheadofabreakwatershouldhaveamassgreaterthanthevaluegivenbyequation (1.7.1). Hudson proposed increasingmass by about 10% in the case of rubble stones and about 30% in the caseofconcreteblocks. However,becausethisisthoughttobeinsufficient, it ispreferabletouserubblestonesorconcreteblockswithamassatleast1.5timesthevaluegivenbyequation (1.7.1).Kimuraetal.36)haveshownthat,inacasewhereperpendicularincidentwavesactonthebreakwaterhead,thestablemasscanbeobtainedbyincreasingtherequiredmassofthebreakwatertrunkby1.5times.Incaseofobliqueincidenceat45º,inthebreakwaterheadontheuppersiderelativetothedirectionofincidenceofthewaves,thenecessaryminimummassisthesameasfor0ºincidence,whereas,onthelowersideofthebreakwaterhead,stabilityissecuredwiththesamemassastheinthebreakwatertrunk.

(10)SubmergedArmorUnitsSincetheactionofwavesonaslopingbreakwaterbelowwatersurfaceisweakerthanabovethewatersurface,themassofstonesorconcreteblocksmaybereducedatdepthsgreaterthan1.5H1/3belowthestillwaterlevel.

(11)CorrectionforWaveDirectionIncaseswherewavesactobliquely to thebreakwater alignment, theextent towhich the incidentwaveangleaffectsthestabilityofthearmorstoneshasnotbeeninvestigatedsufficiently.However,accordingtotheresultsofexperimentscarriedoutbyVandeKreeke,37)inwhichthewaveanglesof0º,i.e.,directionofincidenceisperpendicular to thebreakwater alignment, 30º, 45º, 60º and90º, i.e., directionof incidence isparallel to thenormallinewereadopted,thedamagerateforawavedirectionof45ºorsmallerismore-or-lessthesameasthatforawavedirectionof0º,andwhenthewavedirectionexceeds60º,thedamageratedecreases.Consideringtheseresults,whentheincidentwaveangleis45ºorless,therequiredmassshouldnotbecorrectedforwavedirection.Moreover,Christensenetal.38)haveshownthatstability increaseswhen thedirectionalspreadingofwaves islarge.

(12)StrengthofConcreteBlocksIncaseofdeformedshapeconcreteblock,itisnecessarynotonlytoensurethattheblockhasamasssufficienttobestableforthevariablesituationinrespectofwaves,butalsotoconfirmthattheblockitselfhassufficientstructuralstrength.

(13)StabilityofArmorBlocksinReefAreaIngeneral,areefrisesupatasteepslopefromtherelativelydeepsea,andformsarelativelyflatandshallowseabottom.Consequently,whenalargewaveentersatsuchareef,itbreaksaroundtheslope,andthentheregeneratedwavesafterwardpropagateoverthereefintheformofsurge.Thecharacteristicsofwavesoverareefarestronglydependentonnotonlytheincidentwaveconditionsbutalsothewaterdepthoverthereefandthedistancefromtheshoulderofthereef.Thestabilityofwave-dissipatingconcreteblockssituatedonareefalsovariesgreatlyduetothesamereasons.Thereforethecharacteristicsoverareefaremorecomplicatedthanthatingeneralcases.Thestabilityofwave-dissipatingconcreteblockssituatedonareefmustthusbeexaminedbasedeitheronmodelexperimentsmatchingtheconditionsinquestionoronfieldexperiencesforsiteshavingsimilarconditions.

(14)StabilityofWave-dissipatingBlocksonLowCrestSlopingBreakwaterForalowcrownslopingbreakwaterwithwave-dissipatingblocksandwithoutsupportingwall,itisnecessarytonotethatthewave-dissipatingblocksarounditscrownareeasilydamagedbywaves.39)Forexample,fordetachedbreakwater composedofwave-dissipatingblocks, unlike a caissonbreakwater coveredwithwave-dissipatingblocks,thereisnosupportingwallatthebackandthecrownisnothigh.Thismeansthattheconcreteblocksnearthecrowninparticularattherearareeasilydamaged,andindeedsuchcasesofblockdamagehavebeenreported.Inthecaseofadetachedbreakwater,itispointedoutthatsomekindofconcreteblocksattherearofthecrownshouldhavealargersizecomparedtotheoneatthefrontofthecrown.

(15)StabilityofBlocksonSteepSlopeSeabedIncaseswherethebottomslopeissteepandwavesbreakinaplungingwaveform,alargewaveforcemayactontheblocks,dependingontheirshapes.Therefore,appropriateexaminationshouldbecarriedout,consideringthisfact.40)

(16)High-densityBlocksTherequiredmassofblocksthataremadeofhigh-densityaggregatemayalsobedeterminedusingtheHudson’sformulawiththestabilitynumbershowninequation (1.7.1).Asshownintheequation,high-densityblockshaveahighstability,soastablearmorlayercanbemadeusingrelativelysmallblocks.41)

(17)EffectofStructuralConditionsThestabilityofwave-dissipatingblocksvariesdependingonstructuralconditionsandonthemethodofplacement,suchasregularorrandomplacementetc.Accordingtotheresultsofexperimentsunderconditionsofrandomplacementovertheentirecrosssectionandregulartwo-layerplacementonastonecore,theregularplacementwithgoodinterlockinghadremarkablyhigherstabilityinalmostallcases.32)Provided,however,thatifthelayer


–417–

thicknessoftheblocksisminimalandthepermeabilityofthecorematerialislow,conversely,thestabilityoftheblocksdecreasesinsomecases.42) Thestabilityofwave-dissipatingblocksisalsoaffectedbythecrownwidthandcrownheightoftheblocks.Forexample,accordingtotheresultsofanumberofexperiments,thereisatendencyofhavinggreaterstabilitywhenthecrownwidthandthecrownheightaregreater.

(18)StandardMethodofHydraulicModelTestsThe stability of concrete blocks is influenced by a very large number of factors, and so it has still not beensufficientlyelucidated. Thismeansthatwhenactuallyverifyingtheperformance, it isnecessarytocarryoutstudiesusingmodel experiments, and it is needed toprogressively accumulate the results of such tests. Thefollowingpointsshouldbenotedwhencarryingoutmodelexperiments.

① Itisstandardtocarryoutexperimentsusingrandomwaves.

② For eachparticular setof conditions, theexperiment shouldbe repeatedat least three times i.e.,with threedifferentwavetrains.However,whentestsarecarriedoutbysystematicallyvaryingthemassandotherfactorsandalargeamountofdatacanbeacquired,onerunforeachtestconditionwillbesufficient.

③ Itisstandardtostudytheactionof1000wavesintotalofthreerunsforeachwaveheightlevel.Evenforthesystematicexperiments,itisdesirabletoapplymorethan500wavesorso.

④ Forthedescriptionoftheextentofdamage,inadditiontothedamageratiowhichhasbeencommonlyusedinthepast,thedeformationlevelortherelativedamagelevelmayalsobeused.Thedeformationlevelissuitablewhenitisdifficulttocountthenumberofarmorstonesorconcreteblocksthathavemoved,whilethedegreeofdamageissuitablewhenonewishestorepresentthedamagetowave-dissipatingblocks.Thedamagerateistheratioofthenumberofdamagedarmorunitsinaninspectionareatothetotalnumberofarmorunitsinthesameinspectionarea.Theinspectionareaistakenfromtheelevationofwaverunuptowhicheverisshallower,thedepthof1.5Hbelowthestillwaterlevelortothebottomelevationofthearmorlayer,wherethewaveheightHisinverselycalculatedfromtheHudson’sformulabyinputtingthemassofarmorunits.However,forthedeformationlevelandthedegreeofdamage,thereisnoneedtodefinetheinspectionarea.Forevaluatingthedamagerate,anarmorblockisjudgedtobedamagedifithasmovedoveradistanceofmorethanabout1/2to1.0timesitsheight.

(19)KDValueProposedbyC.E.R.C.Table 1.7.2showstheKDvalueofarmorstonesproposedbytheCoastalEngineeringResearchCenter,C.E.R.C.,oftheUnitedStatesArmyCorpofEngineers.Thisvalueisproposedforthebreakwatertrunk,partsotherthanthebreakwaterhead,inthe1984EditionoftheC.E.R.C.’sShore Protection Manual.43)Inthetable,thevaluesnotinparenthesisarebasedonexperimentresultsbyregularwaves,anditisconsideredthatthosecorrespondsto5%orlessofthedamagerateduetoactionofrandomwaves.Thevaluesinparenthesesareestimatedvalues.Forexample,thevalue(1.2)forroundedrubblestoneswhicharerandomlyplacedintwo-layerunderthebreakingwaveconditionsisgivenasthevaluewhichishalfof2.4,becausetheKDvalueoftwo-layerangularrubblestonesunderthebreakingwavesconditionis1/2thatunderthenon-breakingwaveconditions. However, incaseswherethewaveheightofregularwavescorrespondstothesignificantwaveheight, thewavewhichisclosetothemaximumwaveheightofrandomwavesactscontinuouslyunderthebreakingwavecondition in the regularwaveexperiments. Therefore, the regularwaveexperimentunder thebreakingwaveconditionfallsintoanextremelyseverestateincomparisonwiththatunderthenon-breakingwaveconditions.Inrandomwavesexperiments,asdescribedpreviously,itisconsideredthatsolongasthesignificantwaveheightisastandard,asthebreakingwaveconditionsgetssevere,conversely,KDhasatendencytoincrease.Thus,atleastitisnotnecessarytoreducethevalueofKD underthebreakingwaveconditions.

Table 1.7.2 KD Value of Rubble Stones Proposed by C.E.R.C. (Breakwater Trunk)

Typeofarmor Numberoflayers Placementmethod

KDcotα

Breakingwaves Non-breakingwaves

Rubblestones(rounded) 23ormore

Random″

(1.2)(1.6)

2.4(3.2)

1.5–5.0″

Rubblestones(angular) 23ormore

″″

2.0(2.2)

4.0(4.5)

″″

()showsestimatedvalues.

–418–


1.7.2 Required Mass of Armor Stones and Blocks in Composite Breakwater Foundation Mound against Waves

(1)GeneralTherequiredmassofarmorstonesandblockscoveringthefoundationmoundofacompositebreakwatervariesdependingonthewavecharacteristics,thewaterdepthwherethefacilityisplaced,theshapeofthefoundationmoundsuchasthickness,frontbermwidthandslopeangleetc.,andthetypeofarmorunit,theplacementmethod,andtheposition,breakwaterheadorbreakwatertrunketc.Inparticular,theeffectsofthewavecharacteristicsand the foundationmoundshapearemorepronounced than thaton thearmorstonesandblocksonaslopingbreakwater.Adequateconsiderationshouldalsobegiventotheeffectsofwaveirregularity.Accordingly,therequiredmassofarmorstonesandblocksonthefoundationmoundofcompositebreakwatershallbedeterminedbyperforminghydraulicmodelexperimentsorpropercalculationsusinganappropriateequationinreferencewiththeresultsofpastresearchandactualexperiencesinthefield.Provided,however,thatthestabilityofthearmorunitscovering thefoundationmoundofacompositebreakwater isnotnecessarilydeterminedpurelyby theirmass.Dependingonthestructureandthearrangementofthearmorunitsitmaybepossibletoachievestabilityevenwhenthearmorunitsarerelativelysmall.

(2)BasicEquationforCalculationofRequiredMassAstheequationforcalculationoftherequiredmassofarmorstonesandblocksinthefoundationmoundofacompositebreakwater,Hudson’sformulawiththestabilitynumberNS,asshowninthefollowingequation,canbeusedinthesamemanneraswitharmorstonesandblocksonslopingbreakwater.Inthisequation,thesymbolγisapartialsafetyfactorforitssubscript,andthesubscriptskanddshowthecharacteristicvalueanddesignvalue,respectively.ForthepartialsafetyfactorsγNS andγH intheequation,1.0maybeused.Thispartialsafetyfactoristhevalueincaseswherethelimitvalueofthedamagerateis1%orthelimitvalueofthedegreeofdamageis0.3.

(1.7.1)

This equationwaswidely used as the basic equation for calculating the requiredmass of the foundationmounds of uprightwalls byBrebner andDonnelly.44) In Japan, it is also calledBrebner-Donnelly’s formula.Becauseithasacertaindegreeofvalidity,evenfromatheoreticalstandpoint,itcanalsobeusedasthebasicequationforcalculatingtherequiredmassofarmorunitonthefoundationmoundofacompositebreakwater.45)Provided,however,thatthestabilitynumberNS variesnotonlywiththewaterdepth,thewavecharacteristics,theshapeofthefoundationmound,andthecharacteristicsofthearmorunits,butalsowiththepositionofplacement,breakwatertrunk,breakwaterheadetc.Therefore,itisnecessarytoassignthestabilitynumberNSappropriatelybasedonmodelexperimentscorrespondingtotheconditions.Moreover,thewaveheightusedintheperformanceverification is normally the significantwave height, and thewaves used in themodel experiments should berandomwaves.

(3)StabilityNumberforArmorStonesThestabilitynumberNS maybeobtainedusingthemethodproposedbyInagakiandKatayama,46)whichisbasedontheworkofBrebnerandDonnellyandpastdamagecaseofarmorstones.However,thefollowingformulasproposedbyTanimotoetal.45)arebasedonthecurrentvelocityinthevicinityofthefoundationmoundandallowtheincorporationofavarietyofconditions.TheseformulashavebeenextendedbyTakahashietal.47)soastoincludetheeffectsofwavedirection,andthushavehighapplicability.

(a) ExtendedTanimoto’sformulas

(1.7.8)

(1.7.9)

(1.7.10)

(1.7.11)

where h' :waterdepthatthecrownofrubblemoundfoundationexcludingthearmorlayer(m)(seeFig.

1.7.4) :inthecaseofnormalwaveincidence,thebermwidthoffoundationmoundBM (m)


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inthecaseofobliquewaveincidence,eitherBM orB'M ,whichevergivesthelargervalueof(κ2)B(seeFig. 1.7.4)

L' :wavelengthcorrespondingtothedesignsignificantwaveperiodatthewaterdepthh' (m) αs :correctionfactorforwhenthearmorlayerishorizontal(=0.45) β :incidentwaveangle,anglebetweenthelineperpendiculartothebreakwaterfacelineandthe

wavedirection,noanglecorrectionof15ºisapplied(seeFig. 1.7.5) H1/3 :designsignificantwaveheight(m)

Thevalidityoftheaboveformulashavebeenverifiedforthebreakwatertrunkforobliquewaveincidencewithanangleofincidenceofupto60º.

Shoreward

Foot protection blocksFoot protection blocks

Armor unitsArmor units

Upr

ight

sect

ion

Rubble mound

Seaward

hh'

dBM

BM'

hC

Fig. 1.7.4 Standard Cross Section of a Composite Breakwater and Notations

Breakwater head

Breakw

ater tr

unk

β

Fig. 1.7.5 Effects of Shape of Breakwater Alignment and Effects of Wave Direction

(b)StabilityNumberWhenaCertainAmountofDamageisPermittedSudoetal.havecarriedoutstabilityexperimentsforthespecialcasesuchthatthemoundislowandnowavebreakingoccurs.TheyinvestigatedtherelationshipbetweenthenumberofwavesN andthedamagerate,andproposedthefollowingequationthatgivesthestabilitynumberNS*foranygivennumberofwavesN andanygivendamagerateDN (%).

(1.7.12)

whereNS isthestabilitynumbergivenbytheTanimoto’sformulawhenN =500andthedamagerateis1%.Intheperformanceverification,itisnecessarytotakeN =1000consideringtheprogressofdamage,whilethedamagerate3%to5%canbeallowedfora2-layerarmoring.IfN =1000andDN =5%,thenNS*=1.44NS.Thismeansthattherequiredmassdecreasestoabout1/3ofthatrequiredforN =500andDN =1%.

(4)StabilityNumberforConcreteUnitsThestabilitynumberNS forconcreteblocksvariesaccordingtotheshapeoftheblockandthemethodofplacement.Itisthusdesirabletoevaluatethestabilitynumberbymeansofhydraulicmodelexperiments.49),50)Whencarryingoutsuchexperiments,itisbesttoemployrandomwaves.

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BasedonthecalculationmethodproposedbyTanimotoetal.,45)Fujiikeetal.51)newlyintroducedreferencestability number, which is a specific value for blocks, and separating the termswhich is determined by thestructuralconditionsofthecompositebreakwateretc.,andthen,presentedthefollowingequationregardingthestabilitynumberforarmorblocksincaseswherewaveincidenceisperpendicular.

(1.7.13)

refer(1.7.9)

refer(1.7.10)

(1.7.14)

where NS0 :referencestabilitynumber A :constantdeterminedbasedonwaveforceexperiments(=0.525)

(5)ConditionsforApplicationofStabilityNumbertoFoundationMoundArmorUnitsIncaseswherethewaterdepthabovethearmorunitsonthemoundisshallow,wavebreakingoftencausesthearmor units to become unstable. Therefore, the stability number for foundationmound armor units shall beappliedonlywhenh’/H1/3>1,anditisappropriatetousethestabilitynumberforarmorunitsonaslopeofaslopestructurewhenh’/H1/3≤1.ThestabilitynumberforarmorstonesintheTanimoto’sformulashavenotbeenverifiedexperimentallyincaseswhereh’/H1/3issmall.Accordingly,whenh’/H1/3isapproximately1,itispreferabletoconfirmthestabilitynumberbyhydraulicmodelexperiments. Ontheotherhand,Matsudaetal.52)carriedoutmodelexperimentsinconnectionwitharmorblocks,includingthecaseinwhichh’/H1/3issmallandimpulsivewavesactontheblocks,andproposedamethodthatprovidesalowerlimitofthevalueofκcorrespondingtothevalueofαIinthecasewheretheimpulsivebreakingwaveforcecoefficientαIislarge.

(6)ArmorUnitsThicknessTwo-layers are generally used for armor stones. It may be acceptable to use only one layer provided thatconsiderationisgiventoexamplesofarmorunitsconstructionandexperiencesofdamagedarmorunits.Italsomaybepossibletouseonelayerbysettingtheseveredamagerateof1%forN=1000actingwavesinequation (1.7.12).Onelayerisgenerallyusedforarmorblocks.However,twolayersmayalsobeusedincaseswheretheshapeoftheblocksisfavorablefortwo-layerplacementorseaconditionsaresevere.

(7)ArmorUnitsforBreakwaterHeadAt theheadofabreakwater,strongcurrentsoccur locallynear thecornersat theedgeof theuprightsection,meaningthatthearmorunitsbecomeliabletomove.Itisthusnecessarytoverifytheextenttowhichthemassofarmorunitsshouldbeincreasedatthebreakwaterheadbycarryingouthydraulicmodelexperiments.Ifhydraulicmodelexperimentsarenotcarriedout,itshouldincreasethemasstoatleast1.5timesthatatthebreakwatertrunk.Astheextentofthebreakwaterheadinthecaseofcaissontypebreakwater,thelengthofonecaissonmaybeusuallyadopted.ThemassofthearmorstonesatthebreakwaterheadmayalsobecalculatedusingtheextendedTanimoto’sformula.Specifically,forthebreakwaterhead,thevelocityparameterκ inequation (1.7.9)shouldberewrittenasfollows:

(1.7.15)

(1.7.16)

Notehoweverthatifthecalculatedmassturnsouttobelessthan1.5timesthatforthebreakwatertrunk,itispreferabletosetitto1.5timesthatforthebreakwatertrunk.


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(8)ArmorUnitsatHaborSideItispreferabletodecidethenecessityandrequiredmassofarmorunitsattheharborside,notonlyreferringtopastexamples,butalsoperforminghydraulicmodelexperimentsifnecessaryandconsideringthewavesattheharborside,thewaveconditionsduringconstructionworkandwaveovertoppingetc.

(9)ReductionofMassofArmorTheequationsforcalculationoftherequiredmassofarmorunitsarenormallyapplicabletothehorizontalpartsandthetopofslope.Incaseswherethemoundthicknessisminimal,armorunitsoftheentireslopehavethesamemassinmanycases.However,incaseswherethemoundisthick,themassofarmorunitsplacesontheslopeindeepwatermaybereduced.

(10)FoundationMoundArmorUnitsinBreakwatersCoveredwithWave-dissipatingBlocksInthecaseofbreakwaterscoveredwithwave-dissipatingblocks,theupliftpressureactingonthearmorandthecurrentvelocities in thevicinityof themoundare smaller than thoseofconventional compositebreakwaters.Fujiikeetal.51)carriedoutmodelexperimentsinconnectionwiththestabilitiesofboththearmorunitsoftheconventionalcompositebreakwatersandthebreakwaterscoveredwithwave-dissipatingblocks,andproposedamethodofmultiplicatingequation (1.7.9)bythecompensationrate.Namely,

(1.7.17)

where CR :breakwatershapeinfluencefactor,itmaybeused1.0forconventionalcompositebreakwaters

approximately0.4forbreakwaterscoveredwithwave-dissipatingblocks.

(11)FlexibleArmorUnitsUseofbag-typefootprotectionunitswhichconsistofsyntheticfibernetfilledwithstonesasthearmorunitsonthefoundationmoundhasvariousadvantages:largestonesarenotrequired,andmoundlevelingisnotvirtuallyneededbecausetheyhavehighflexibilityandcanadheretotheirregularseabed.Shimosakoetal.53)proposedamethodofcalculatingtherequiredmassofarmorunitsonthefoundationmoundusingbag-typefootprotectionunits,andalsoexaminedtheirdurability.

1.7.3 Required Mass of Armor Stones and Blocks against Currents

(1)GeneralTherequiredmassofrubblestonesandotherarmormaterialsforfoundationmoundstobestableagainstwatercurrentsmaybegenerallybedeterminedbyappropriatehydraulicmodelexperimentsorcalculatedusing thefollowingequation.Inthisequation,thesymbolγisapartialsafetyfactorforitssubscript,andthesubscriptskanddshowthecharacteristicvalueandthedesignvalue,respectively.

(1.7.18)

where M :stablemassofrubblestonesorotherarmormaterial(t) ρr :densityofrubblestonesorotherarmormaterial(t/m3) U :currentvelocityofwateraboverubblestonesorotherarmormaterial(m/s) g :gravitationalacceleration(m/s2) y :Isbash’sconstant,forembeddedstones,1.20;forexposedstones,0.86 Sr :specificgravityofrubblestonesorotherarmormaterialrelativetowater θ :slopeangleinaxialdirectionofwaterchannelbed(º)

Thedesignvaluesintheequationmaybecalculatedbyusingthefollowingequations.ForthepartialsafetyfactorsγU andγy,1.0maybeused.

Ud =γU Uk,yd =γy yk

ThisequationwasproposedbytheC.E.R.C.forcalculationofthemassofrubblestonesrequiredtopreventscouringbytidalcurrentsandiscalledIsbash’sformula.43)Asalsoshownintheequation,attentionshouldbegiventothefactthattherequiredmassofarmorunitsagainstcurrentsincreasesrapidlyasthecurrentvelocityincreases.Therequiredmassalsovariesdependingontheshapeanddensityofthearmorunitsetc.

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(2)Isbash’sConstantEquation (1.7.18)wasderivedconsideringthebalanceofthedragforceoftheflowactingonasphericalobjectonaslopeandthefrictionresistanceforce.TheconstantyisIsbash’sconstant.Thevaluesof1.20and0.86forembeddedstonesandexposedstones,respectively,aregivenbyIsbash,andarealsocitedinReference54).Itshouldbenotedthat,becauseequation (1.7.18)wasobtainedconsideringthebalanceofforcesinasteadyflow,itisnecessarytouserubblestoneswithalargermassintheplacewherestrongvorticeswillbegenerated.

(3)ArmorUnitsonFoundationMoundatOpeningsofTsunamiProtectionBreakwatersIwasakietal.55)conductedexperimentson2-dimensionalsteadyflowsforthecaseinwhichdeformedconcreteblocksareusedasthearmorunitsonafoundationmoundintheopeningofthesubmergedbreakwatersoftsunamiprotectionbreakwater,andobtainedavalueof1.08forIsbash’sconstantinequation (1.7.18).Tanimotoetal.56)carriedouta3-dimensionalplaneexperimentfortheopeningofbreakwaters,clarifyingthe3-dimensionalflowstructureneartheopening,andalsorevealedtherelationshipbetweenIsbash’sconstantandthedamagerateforthecaseswherestonematerialsanddeformedconcreteblocksareusedasthearmorunits.


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1.8 Scouring and Washing-outPublic NoticePerformance Criteria Common to Structural Members

Article 22 3Incaseswheretheeffectsofscouringoftheseabedandsandoutflowontheintegrityofstructuralmembersmayimpairthestabilityofthefacilities,appropriatecountermeasuresshallbetaken.

[Commentary]

(1)ScouringandWashout(serviceability)Incaseswherescouringofthefoundationoffacilitiesconcernedandgroundandoutflowofsandfromthegroundbehindstructuresmightimpairthestabilityofthefacilities,appropriatecountermeasuresagainstscouringandcountermeasuresagainstwashoutmustbetaken,consideringthestructuraltypeoftheobjectivefacilities.

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2 Foundations2.1 General Comments

(1)Thefoundationstructuresof theport facilitiesshallbeselectedappropriately,givingdueconsideration to theimportanceofthefacilitiesandsoilconditionsofthefoundationground.

(2)Whenthestabilityofthefoundationstructuresseemstobeanobstacle,countermeasuressuchaspilefoundationorsoilimprovement,etc.shallbeappliedasnecessary.

(3)When the foundation ground is soft, excessive settlement or deformationmay arise owing to the lack of thebearingcapacity.Whenthefoundationgroundconsistsofloosesandysoil,liquefactionduetoactionofgroundmotioncausesthestructurefailureorsignificantlydamageitsfunctions.Insuchcases,thestressinsubsoilbytheweightofstructuresneedstobereducedorthefoundationgroundshouldbeimproved.

(4)Forthestabilityoffoundations,2.2 Shallow Spread Foundations,and2.3 Deep Foundations,or3 Stability of Slopes canbeusedasreference.Forsettlementoffoundations,2.5 Settlement of Foundations,andforliquefactiondue to actionofgroundmotion, Part II,Chapter 6 Ground Liquefaction canbeusedas reference. For theperformance verification of pile foundations,2.4 Pile Foundations can be used as reference. In caseswhereit isnecessary toconduct theperformanceverification forgroundmotion, theverificationshallbeperformedcorrespondingtothecharacteristicsoftherespectivefoundations.

(5)MethodsofReducingGroundStressThefollowingaremethodsofreducinggroundstressduetotheweightofstructures.

①Reductionoftheweightofthestructureitself

②Expansionoftheareaofthebottomofthestructure

③UseofapilefoundationShearstressduetothefacilitiesmaybereducedbythecounterweightmethod.

(6)MethodofSoilImprovementFormethodofsoilimprovement,4 Soil Improvement Methods canbeusedasreference.

2.2 Shallow Spread Foundations2.2.1 General

(1)Whentheembedmentdepthofthefoundationislessthantheminimumwidthofthefoundation,thefoundationmaygenerallybeexaminedasashallowspreadfoundation.

(2)Ingeneral,thebearingcapacityofafoundationisthesumofthebottombearingcapacityandthesideresistanceofthefoundation.Bottombearingcapacityisdeterminedbythevalueofthepressureappliedtothefoundationbottom considered necessary to cause plastic flow in the ground. The side resistance of a foundation is thefrictionalresistanceorthecohesionresistanceactingbetweenthesidesofthefoundationandthesurroundingsoil.Althoughconsiderableresearchhasbeendoneonthebottombearingcapacityoffoundations,relativelylittleresearchhasbeendoneonsideresistance.Iftheembedmentdepthofthefoundationislessthantheminimumwidthofthefoundation,inthecaseofso-calledshallowspreadfoundations,themagnitudeofthesideresistancewillbesmallincomparisonwiththatofthebottombearingcapacity.Therefore,itisnotnecessarytoconsiderthesideresistanceinsuchcases.

(3)Whenaneccentricandinclinedactionactsonthefoundation,2.2.5 Bearing Capacity for Eccentric and Inclined Actions canbeusedasreference.

2.2.2 Bearing Capacity of Foundations on Sandy Ground

(1)Thefollowingequationcanbeusedtocalculatethedesignvalueofthebearingcapacityofthefoundationsonsandyground.Inthiscase,appropriatevaluescorrespondingtothecharacteristicsofthefacilitiescanbeadoptedasthepartialfactors.Ingeneral,0.4orlesscanbeconsideredanappropriatepartialfactorγR.

(2.2.1)where

qd :designvalueoffoundationbearingcapacityconsideringbuoyancyofsubmergedpart(kN/m2) γR :partialfactorforbearingcapacityofsandyground


–427–

β :shapefactoroffoundation,seeTable 2.2.1ρ1dg :designvalueofunitweightofsoilofgroundbelowfoundationbottomorunitweightinwater,

ifsubmerged(kN/m3) B :minimumwidthoffoundation(m)

Nrd,Nqd :designvaluesobtainedbymultiplyingpartialfactorsγNqandγNγ bythecharacteristicvaluesofthebearingcapacityfactorNqkandNγk(seeFig. 2.2.1),1)respectively.Thecharacteristicvaluesofthebearingcapacityfactorareexpressedbythefollowingequations.

(Prandtl’ssolution)

(Meyerhof’ssolution)

ρ2dg :designvalueofunitweightofsoilofgroundabovefoundationbottom,orunitweightinwater,ifsubmerged(kN/m3)

D :embedmentdepthoffoundationinground(m)

(2)Whentheactionsonthefoundationincrease,first,settlementofthefoundationoccursinproportiontotheactions.However,whentheactionsreachacertainvalue,settlementincreasessuddenlyandshearfailureofthegroundoccurs.Theintensityoftheloadrequiredtocausethisshearfailurewhichisobtainedbydividingtheloadbythecontactareaiscalledtheultimatebearingcapacityofthefoundation.ThebearingcapacityofthefoundationcanbecalculatedbymultiplyingtheultimatebearingcapacityobtainedfromthebearingcapacityformulabythepartialfactorγR.

Table 2.2.1 Shape Factors

Shapeoffoundation Continuous Square Round Rectangularβ 1 0.8 0.6 1–0.2(B/L)

B: lengthofshortsideofrectangle,L:lengthoflongsideofrectangle

1

10

100

0 10 20 30 40 50

Nqk Nγk

Cha

ract

eris

tic v

alue

s of b

earin

g ca

paci

ty fa

ctor

t Nqk

and

Nγk

φφCharacteristic value of angle of shear resistance k (º)

Fig. 2.2.1 Relationship between Bearing Capacity Factors Nrk and Nqk and Angle of Shear Resistance φk

–428–


2.2.3 Bearing Capacity of Foundations on Cohesive Soil Ground

(1) Incalculationsofthedesignvaluesforfoundationsofcohesivesoilgroundincaseswheretheundrainedshearstrength increases linearlywithdepth, the following equation canbeused. In this case, an appropriate valuecorrespondingtothecharacteristicsofthefacilitiesshallbeselectedforthepartialfactorγR.

(2.2.2)

where qd :designvalueoffoundationbearingcapacityconsideringbuoyancyofsubmergedpart(kN/m2) γR :partialfactorforbearingcapacityofcohesivesoilground Nc0d :designvalueofbearingcapacityfactorforcontinuousfoundation n :shapefactoroffoundation,seeFig. 2.2.2 B :minimumwidthoffoundation(m) L :lengthoffoundation c0d :designvalueofundrainedshearstrengthofcohesivesoilatbottomoffoundation(kN/m2) ρ2dg :designvalueofunitweightofsoilofgroundabovefoundationbottom,orunitweightinwater,

ifsubmerged(kN/m3) D :embedmentdepthoffoundationinground(m)

(2)Astheundrainedshearstrengthofcohesivesoilgroundinportareasusuallyincreaseslinearlywithdepth,thebearing capacity of foundation should be calculated by the equation that takes account of the effect of shearstrengthincrease.

(3)Equation for Calculating Design Value of Bearing Capacity of Cohesive Soil Ground Considering StrengthIncreaseinDepthDirection ThedesignvalueNc0dofthebearingcapacityfactorinequation (2.2.2)canbecalculatedusingFig. 2.2.2.Here,kisthestrengthincreaserateinthedepthdirection.Ifthesurfacestrengthisassumedtobec0,thestrengthatdepthzisexpressedbyc0+kz.AsthepartialfactorforthebearingcapacityγR,anappropriatevalueof0.66orlesscanbeusedgenerally,butincaseswherethereisapossibilitythatslightsettlementordeformationofthegroundmayremarkablyimpairthefunctionsofsuperstructure,asinthecaseofcranefoundations,avalueofnomorethan0.4shallbeused.

12

10

8

6

4

4

2

20

00

1 3 5

0.05

0.10

0.30

0.25

0.20

0.15 n

n

kkB/c0k

Nc0k

Nc0k

z

c0

kz

Load intensity

B

Fig. 2.2.2 Relationship of Bearing Capacity factor Ncok of Cohesive Soil Ground in which Strength Increases in Depth Direction and Shape Factor n


–429–

(4)PracticalEquationforCalculatingDesignValueofBearingCapacityBasedonthebearingcapacityfactorsshowninFig. 2.2.2,thedesignvalueofthebearingcapacityoffoundationsincaseofcontinuousfoundationscanbecalculatedusingthepracticalequationshowninequation (2.2.3)intherangewherekkB/c0k≤4.Thesymbolsusedarethesameasinequation(2.2.2).

(provided,however,thatkkB/c0k≤4) (2.2.3)

2.2.4 Bearing Capacity of Multi-layered Ground

(1)Examinationofstabilityforthebearingcapacitywhenthefoundationgroundhasamulti-layeredstructurecanbeperformedbycircularslipfailureanalysis.Assumingtheoverburdenpressureabovethelevelofthefoundationbottomasthesurcharge,circularslipfailureanalysisisperformedbythemodifiedFelleniusmethodforanarcpassingthroughtheedgeofthefoundation,asshowninFig. 2.2.3.AsthepartialfactorγRfortheanalysismethod,0.66orlesscanbeusedgenerally,butincaseswheresettlementwillhavealargeeffectonthefunctionsofthefacilitieslikecrane,itispreferabletouseavalueofnomorethan0.4.

Soil layer 1

Soil layer 2

Soil layer 3

Soil layer 4

B

Fig. 2.2.3 Calculation of Bearing Capacity of Multi-layered Ground by Circular Slip Failure Analysis

(2)IfthecohesivesoillayerthicknessH issignificantlylessthanthesmallestwidthofthefoundationB (i.e.,H <0.5B),apunchingshearfailure,inwhichthecohesivesoillayerissqueezedoutbetweenthesurchargeplaneandthebottomofcohesivesoillayer,isliabletooccur.Thebearingcapacityagainstthiskindofsqueezed-outfailurecanbecalculatedbythefollowingequation4)

(2.2.4)

where qd :design value of bearing capacity of foundation considering the buoyancy of the submerged

part（kN/m2） B :smallestwidthoffoundation（m） H :thicknessofcohesivesoillayer（m） cud :designvalueofmeanundrainedshearstrengthinlayerofthicknessH（kN/m2） ρ2dg :designvalueofunitweightofsoilabovetheleveloffoundationbottomorunitweightinwater,

ifsubmerged（kN/m3） γR :partialfactorforbearingcapacity D :embeddeddepthoffoundation（m）

2.2.5 Bearing Capacity for Eccentric and Inclined Actions

(1)Examinationofthebearingcapacityforeccentricandinclinedactionsactingonthefoundationgroundofgravity-typestructurescanbeperformedbycircularslipfailureanalysiswiththesimplifiedBishopmethodusingthefollowing equation. In this equation, the symbol γ is the partial factor for its subscript, and the subscripts k anddindicatethecharacteristicvalueanddesignvalue,respectively.Inthiscase,thepartialfactorshallbeanappropriatevaluecorrespondingtothecharacteristicsofthefacilities.Itisnecessarytosetthestrengthconstantoftheground,theformsoftheactions,andotherfactorsappropriatelyconsideringthestructuralcharacteristicsofthefacilities.

–430–


(2.2.5)

where R :radiusofincircularslipfailure(m) cd :incaseofcohesivesoilground,designvalueofundrainedshearstrength,andincaseofsandy

ground,designvalueofapparentcohesionindrainedcondition(kN/m2) W’d :designvalueofeffectiveweighttodiscretesegmentperunitoflength,submergesunitweightif

submerged(kN/m) qd :designvalueofverticalactionfromtopofdiscretesegment(kN/m) θ :angleofbottomofdiscretesegmenttohorizontal(º) φd :incaseofcohesivesoilground,thevalueshallbe0,andincaseofsandyground,designvalue

ofangleofshearresistanceindrainedcondition(º) Wd :designvalueoftotalweightofdiscretesegmentperunitoflength,namelytotalweightofsoil

andwater(kN/m) PHd :designvalueofhorizontalactiononlumpsofearthincircularslipfailure(kN/m) a :armlengthfromthecenterofcircularslipfailureatpositionofactionofanexternalactionH S :widthofdiscretesegment(m) γFf :partialfactorforanalysismethod

Basedonequation (2.2.5),γFf iscalculated,andstabilityisverifiedbytheverificationparameterFf≥1.Thedesignvaluesintheequationcanbecalculatedbythefollowingequations.Provided,however,thatincaseswherepartialfactorsaregivenbystructuraltype,thepartialfactorforthepartconcernedshallbeused.Inothercaseswherepartialfactorsarenotparticularlydesignated,thevalueofthepartialfactorγcanbesetat1.00.

cd =γc ck,W'd =γW' W'k,qd =γq qk,φd =tan–1(γtanφ tanφk),PHd =γPH PHk (2.2.6)

(2)Ingravity-typequaywallsandgravity-typebreakwaters,actionsduetoselfweight,earthpressure,waveforce,andgroundmotionshallbeconsidered.However,theresultantoftheseactionsisnormallybotheccentricandinclined.Therefore,examinationforeccentricandinclinedactionsisnecessaryinexaminationof thebearingcapacityoffoundations.Here,eccentricandinclinedactionmeansanactionwithaninclinationratioequaltoorgreaterthan0.1.

(3)Because normal gravity-type structures are two-layered structureswith a rubblemound layer on foundationground,anexaminationmethodwhichadequately reflects this feature isnecessary.The fact thatcircular slipfailure calculations by theBishopmethod, simplifiedBishopmethod, accurately express stability for bearingcapacity has been confirmed in a series of research results, including laboratorymodel experiments, in-situloadingexperiments,andanalysisoftheexistingbreakwatersandquaywalls,andthismethodisthereforeusedasageneralmethod.5)

(4)AnalysisofBearingCapacitybyCircularSlipFailureAnalysisbasedontheBishopMethodAnalysisthroughcircularslipfailureanalysisbasedontheBishopmethodismoreprecisethantheanalysisbasedon themodifiedFelleniusmethod,exceptwhenaverticalactionexertsonhorizontally layeredsandyground.Therefore,thecircularslipfailureanalysisbytheBishopmethodisappliedundertheconditionthateccentricandinclinedactionsexertact.AsshowninFig. 2.2.4 (a),thestartpointoftheslipsurfaceissetsymmetricalabouttheactingpointofresultantloadtooneofthefoundationedgesthatisclosertotheloadactingpoint.Inthiscase,theverticalactionexertingontherubblemoundisconvertedintouniformlydistributedloadactingonthewidthbetweenforetoeofthebottomandthestartpointoftheslipsurfaceasindicatedinFig. 2.2.4 (b) and(c).Thehorizontalforceisassumedtoactatthebottomofstructure.Whencalculatingthebearingcapacityduringanearthquake,seismicforceisassumednottoactontherubblemoundandtheground.


–431–

(a) (b) (c)

b' b'b'

b'b' b' b'

b'

2b' 2b'

ee

q q

p1 p1p2

B Bb

R R

When subgrade reaction has a trapezoidal distribution; q=

q=p1b4 b'

(p1+p2) 4 b'-

-

B

When subgrade reaction has a triangular distribution;

Combined force of load

Rubblemound

Subsoil

Fig. 2.2.4 Analysis of Bearing Capacity for Eccentric and Inclined Actions

(5)VerificationParameterandPartialFactors

①Theverificationparameter isexpressedby the ratioof theslidingmomentdue toactionsand theweightofearthandtheresistantmomentduetoshearresistance(see3.2.1 Stability Analysis by Circular Slip Failure Surface).Asgeneralvaluesofthepartialfactorsfortheanalysismethod,thevaluesshowninTable 2.2.2canbeused.Provided,however,thatincaseswherepartialfactorsareindicatedbystructuraltype,thepartialfactorforthepartconcernedshallbeused.

②Regardingactionsonbreakwatersduetogroundmotion,fewexamplesofdamageareavailable,andthedegreeofdamage is also small.As the reasons for this, inmanycasesactionsdue togroundmotionarebasicallyequalintheharbordirectionandtheouterseadirection,andlargedisplacementdoesnotoccurduetotheshortdurationoftheaction.Accordingly,examinationofthebearingcapacityduetoactionsofgroundmotionmaybeomittedinthecaseofordinarybreakwaters.Provided,however,thatdetailedexaminationbydynamicanalysisisdesirableforbreakwaterswherestabilityduetoactionsofgroundmotionmaybeaseriousproblem.

Table 2.2.2 Standard Values of Partial Factor γFf in Analysis Method for Bearing Capacity for Eccentric and Inclined Actions (Bishop Method)

Quaywalls Breakwaters

Permanentsituation ≤0.83 –

VariablesituationforLevel1earthquakegroundmotion ≤1.00 –

Variablesituationforwaves – ≤1.00

Note)Incasepartialfactorsareindicatedbystructuraltype,thepartialfactorforthepartconcernedshallbeused.

(6)StrengthParametersforMoundMaterialsandFoundationGround

①MoundmaterialsModelandfieldexperimentsonbearingcapacitysubject toeccentricandinclinedactionshaveverifiedthathigh precision results can be obtained by conducting circular slip failure analyses based on the simplifiedBishopmethod,applyingthestrengthparametersobtainedbytriaxialcompressiontests5).Large-scaletriaxialcompressiontestresultsofcrushedstonehaveconfirmedthatthestrengthparametersoflargediameterparticlesareapproximatelyequaltothoseobtainedfromsimilargrainedmaterialswiththesameuniformitycoefficient6).Therefore,triaxialcompressiontestsusingsampleswithsimilargrainedmaterialsarepreferablyconductedinordertoestimatethestrengthparametersofrubblesaccurately.Ifthestrengthtestsarenotconducted,thevaluesofcohesioncD =20kN/m2andshearingresistanceangleφD =35ºareappliedasthestandardstrengthparametersforrubblesgenerallyusedinportconstructionworks. The above standard values have been determined as safe side values based on the results of large-scaletriaxialcompressiontestsofcrushedstones.Thevalueshavebeenprovenappropriatefromtheanalysisresultsofthebearingcapacityoftheexistingbreakwatersandquaywalls.ItshouldbenotedthatcohesioncD =20kN/m2asastrengthparameteristheapparentcohesion,takingaccountofvariationsoftheshearresistanceangle

–432–


φDofcrushedstonesundervariableconfiningpressures.Fig. 2.2.5 showstheresultsoftriaxialcompressiontestsonvarioustypesofcrushedstonesandrubbles5).Itshowsthatastheconfiningpressureincreases,φDdecreasesduetoparticlecrushing.ThesolidlineinthefigurerepresentsthevalueundertheassumptionthattheapparentcohesioniscD =20kN/m2andtheshearfrictionangleisφD=35º.Here,thedependencyofφDontheconfiningpressureiswelldescribedbytakingtheapparentcohesionintoaccount.Thesestandardvaluescanbeappliedonlytothestonematerialwithanunconfinedcompressivestrengthinthemotherrockof30MN/m2ormore.Ifweakstoneswiththecompressivestrengthofthemotherrockoflessthan30MN/m2areusedasapartofthemound,thestrengthparameterswillbearoundcD=20kN/m2andφD =30º7).

50

45

40

35

30

25

50

100 200 400 800 1400

cD=20kN/m2, D=35゜Test values

Lateral pressureσ3 (kN/m2)

φφD(°)

φφ

Fig. 2.2.5 Relationship between φD and Lateral Confining Pressure σ3 and Apparent Cohesion

②FoundationgroundFoundationssubjecttoeccentricandinclinedactionsoftencauseshallowsurfaceslipfailure.Inthesecases,itisimportanttoevaluatethestrengthnearthesurfaceoffoundationground.Ifthefoundationgroundissandy,thestrengthcoefficientφD isusuallyestimatedfromN-value.Theestimationformulasemployedup tonowhavetendedtounderestimateφDincaseofshallowsandygrounds.Thisisbecausenocorrectionhasbeenmaderegardingtheeffectivesurchargepressurein-situ. Fig. 2.2.6 collates the results of triaxial compression tests on undisturbed sand in Japan and presents acomparative studyof the formulasproposed in thepast.Evenwhen theN-valuesare less than10, shearingresistance angles of around 40º have been obtained. Inmany cases, the bearing capacity for eccentric andinclinedactionsisimportantontheperformanceverificationwhichisnotunderthepermanentsituationbutunderdynamicexternalforcessuchaswaveandseismicforces.Inadditiontotheaboveandbasedontheresultsofbearingcapacityanalysisofthestructuresdamagedinthepast,thevaluesgivenbelowareappliedasthestandardvaluesofφD infoundationground.

SandygroundwithN-valueoflessthan10: φD=40ºSandygroundwithN-valueof10ormore: φD=45º

Ifthegroundconsistsofcohesivesoil,thestrengthmaybedeterminedbythemethodindicatedinPart II, Chapter 3, 2.3.3 Shear Characteristics.


–433–

50

40

301 2 5 10 20 50 100 200 500N-value

Range according to Meyerhof

D(°

)

Triaxial testresults

φφ

D= 20N + 15 according to Osakiφφ

Fig. 2.2.6 Relationship Between N-value and φD Obtained by Triaxial Tests of Undisturbed Sand Samples

–434–


2.3 Deep Foundations2.3.1 General

(1)When thepenetrationdepthof a foundation isgreater than theminimumwidthof the foundation, it shallbeexaminedasadeepfoundation.MeansofdistinguishingthedeepfoundationsdescribedherefrompilefoundationsincludethemethodofjudgingwhetherβL(L:embedmentlengthofpile)≦1ornot,basedoncalculationsbythemethodproposedbyY.L.Chan,see 2.4.5 Static Maximum Lateral Resistance of Piles.

(2)Foundationsofthetypedescribedin(1)generallyincludethewell,pneumaticcaissonandcontinuousundergroundwall.Forpilefoundations,see2.4 Pile Foundations.

(3)Deepfoundationssupportthesuperstructurestablybytransmittingtheactionduetotheheavysuperstructurethroughtheweakupperstratatothestronglowerstrata.Accordingly,itcannormallybeconsideredthatverticalforce is supported by the frictional resistance at the side surfaces of the foundation and the vertical bearingcapacityatthebottom,andthehorizontalforceissupportedbythepassiveresistanceoftheground.

2.3.2 Characteristic Value of Vertical Bearing Capacity

(1)Thecharacteristicvalueoftheverticalbearingcapacityofadeepfoundationshallbesettakingintoaccountthesoilconditions,thestructuraltype,andthemethodofconstruction.

(2)Generally,theverticalbearingcapacityofadeepfoundationcanbedeterminedfromthebearingcapacityofthefoundationbottomand theresistanceof thefoundationsides,asshowninequation (2.3.1).However, incaseswheretheamountofdisplacementand/ordeformationofthefacilitiesmaybeaproblem,thedeformationofdeepfoundationsshouldbeestimatedbyassumingthegroundbehavesasaspring.

(2.3.1)where

quk :characteristicvalueofverticalbearingcapacityofdeepfoundation(kN/m2) qu1k :characteristicvalueofbearingcapacityoffoundationbottom(kN/m2) see2.2.2 Bearing Capacity of Foundations on Sandy Ground,2.2.3 Bearing Capacity of

Foundations on Cohesive Soil Ground qu2k :characteristicvalueofbearingcapacityduetoresistanceoffoundationsides(kN/m2)

(3)The design value of the vertical bearing capacity of deep foundations shall consider a safetymargin in thecharacteristic value of the vertical bearing capacity, as in equation (2.3.2). The characteristic value of thefoundation bottom bearing capacity determined as described in2.2.2 Bearing Capacity of Foundations on Sandy Groundand2.2.3 Bearing Capacity of Foundations on Cohesive Soil Ground,andthepartialfactorγa,whichisusedincaseswherethecharacteristicvalueoftheverticalbearingcapacityisdeterminedusingequation (2.3.3)andequation(2.3.5),asshowninthefollowing,cangenerallybesetat0.4orlessforimportantfacilitiesand0.66orlessforotherfacilities.

(2.3.2)where

qud :designvalueofverticalbearingcapacityofdeepfoundation(kN/m2) quk :characteristicvalueofverticalbearingcapacityofdeepfoundation(kN/m2)

(4)Cautionisrequiredconcerningtheresistanceofthesidesofdeepfoundations,astherearecasesinwhichthesurroundinggroundmaybedisturbedbyconstructionand,asaresult,adequatebearingcapacitybysideresistancecannotbeexpected,dependingonthestructuraltypeandmethodofconstruction.

① Thecharacteristicvalueofthebearingcapacityduetothefrictionalresistanceofthefoundationsidesinsandygroundcanbecalculatedbyequation (2.3.3).

(2.3.3)where

Kak :characteristicvalueofcoefficientofactiveearthpressure(δ=0º),seePart II,Chapter 5, 1 Earth Pressure

γ2k :characteristicvalueofunitweightofsoilaboveleveloffoundationbottom,orsubmergedunitweightifsubmerged(kN/m3)


–435–

D :penetrationdepthoffoundation(m) μk :characteristic value of coefficient of friction between foundation sides and sandy soil,

øk : characteristicvalueofshearresistanceangle(º) B :widthoffoundation(m) L :lengthoffoundation(m)

qu2kinequation(2.3.3),isobtainedbydividingthetotalfrictionresistancebythebottomareaoffoundation.Thetotalfrictionresistanceiscalculatedastheproductofthemeansidefrictionstrength f multiplyingwiththepenetrationdepthD andthetotalcontactsurfaceareabetweenthesandysoilandfoundationsides.Equation(2.3.4)isgenerallyusedtocalculatethemeansidefrictionstrength f correspondingtothepenetrationdepthD.

(2.3.4) Thefrictionanglebetweenthefoundationsidesandsandysoilshouldnotbegreaterthantheshearresistanceangleofsoilφ,anditmaybetakenas(2/3)φforthecasebetweenconcreteandsandysoil.

②Thecharacteristicvalueofbearingcapacityduetothecohesiveresistanceofthefoundationsidesincohesivesoilgroundcanbecalculatedbyequation(2.3.5).

(2.3.5)where

cak :characteristicvalueofmeanadhesion(meanvalueinembeddedpart)(kN/m2)

Dc :penetrationdepthoffoundationbelowgroundwaterlevel(m) B :widthoffoundation(m) L :lengthoffoundation(m)

In caseof deep foundations in cohesive soil ground, there is generally a possibility of drying shrinkageduringsummerinthesoilabovethegroundwaterlevel;therefore,thissoilisnotconsideredtobeaneffectivecontact surface.Accordingly, themeanadhesionca inequation (2.3.5) shouldbe themeanadhesion in theeffectivecontactpart. Aspracticalvaluesofmeanadhesionincohesivesoil,thevaluesinTable 2.3.1canbeusedasreference.

Table 2.3.1 Relationship between Unconfined Compression Strength and Mean Adhesion of Cohesive Soil (kN/m2)

Classofgroundatfoundationside qu caSoftcohesivesoil 20–50 –*)

Mediumcohesivesoil 50–100 6–12Hardcohesivesoil 100–200 12–25Extremelyhardcohesivesoil 200–400 25–30Consolidatedcohesivesoil >400 >30

*Note)withsoftcohesivesoil,sideresistanceshouldnotbeconsidered.

(5)ConsiderationofNegativeSkinFrictionIncaseswherethedeepfoundationpenetratesthroughtheconsolidablegroundandreachesthebearinglayer,itisnecessarytoexaminenegativeskinfrictionactingonthebody.Asthemethodofexaminationinthiscase,2.4.3 [9] Examination of Negative Skin Friction canbeusedasreference.

2.3.3 Horizontal Resistance Force of Deep Foundations

(1)Thecharacteristicvalueofthelateralbearingcapacityofadeepfoundationshallbedeterminedasappropriatetakingintoaccountsoilconditions,structuralcharacteristics,andthemethodofconstruction.

(2)Thelateralbearingcapacityofadeepfoundationisgovernedbythehorizontalsubgradereactionofthefoundationsidesandtheverticalsubgradereactionatthebottomoffoundation.

(3)Thecharacteristicvalueofthehorizontalresistanceforceofdeepfoundationscanbedeterminedfromthepassiveearthpressureandultimatebearingcapacity.

–436–


(4)Thedesignvalueof thehorizontal resistance forceofdeep foundationsshould includea safetymargin in thecharacteristicvalue,asinthefollowingequation.Whenthecharacteristicvalueofthehorizontalresistanceforceofadeepfoundation isobtainedbythemethodpresentedbelow, thepartial factorsshowninTable 2.3.2cangenerallybeused.

(2.3.6)where

Fud :designvalueofhorizontalresistanceforceofdeepfoundation(kN/m2) Fuk :characteristicvalueofhorizontalresistanceforceofdeepfoundation(kN/m2) γa :partialfactor

Table 2.3.2 Partial Factor γa

Resistanceforcebypassiveearthpressure ResistanceforcebyverticalbearingcapacityImportantfacilities 0.66 0.40Otherfacilities 0.90 0.66

(5)CalculationMethodforPerformanceVerification

①Whenaresultantforceatabottomoffoundationactsinsidethecore,namelytheeccentricityoftotalresultantforceactingatthebottomoffoundationiswithinone-sixthofthefoundationwidthfromthecentralaxisofthefoundation,themaximumhorizontalsubgradereactionp1andmaximumverticalsubgradereactionq1canbeestimatedbyassumingthedistributionsofhorizontalandverticalsubgradereactionareassumedasinFig. 2.3.1.

Fig. 2.3.1 When Resultant Force is inside the Core

② AssumptionontheDistributionofSubgradeReactionThedistributionofhorizontal subgrade reaction shown inFig. 2.3.1 maybe assumedasbeing aquadraticparabolawiththesubgradereactionof0atthegroundsurface.Thisassumptionisequivalenttotherelationshipbetweenthedisplacementy andthesubgradereactionp ofequation(2.3.7)whenthefoundationrotatesasarigidbody.

(2.3.7)where

p :subgradereaction（kN/m2） k :rateofincreaseincoefficientofhorizontalsubgradereactionwithdepth（kN/m4） x :depth（m） y :horizontaldisplacementatdepthx（m）


–437–

Whenalineardistributionisassumedforverticalsubgradereactionandaresultantforceactingatthebottomoffoundationisinsidethecore,thedistributionoftheverticalsubgradereactionbecomestrapezoidalasshowninFig. 2.3.1.

③ Conditionswhenverticalresultantisinthecoreandcharacteristicvalueforhorizontalresistanceforceinsuchcases Theconditionsforthecaseinwhichtheverticalresultantatthebottomisinthecoreareexpressedasinequation (2.3.8).

(2.3.8)

Themaximumhorizontalsubgradereactionp1(kN/m2)andthemaximumverticalsubgradereactionq1(kN/m2)inthiscaseareobtainedbyequations (2.3.9) and(2.3.10),respectively.

(2.3.9)

(2.3.10)

Whendeterminingthehorizontalresistanceforceofdeepfoundations,thevaluesofp1andq1obtainedbyequations(2.3.9) and(2.3.10)mustsatisfyequations(2.3.11)and(2.3.12),respectively.

(2.3.11)

(2.3.12)where

l :penetrationdepth(m) 2b :maximumwidthperpendiculartohorizontalforce(m) 2a :maximumlength(m) A :bottomarea(m2) P0 :horizontalforceactingonstructureabovegroundsurface(kN) M0 :momentduetoP0atgroundsurface(kN・m) N0 :verticalforceactingatgroundlevel(kN) k :horizontalseismiccoefficient K' :K'=K2/K1 K1 :rateofincreaseincoefficientofverticalsubgradereaction(kN/m4) K2 :rateofincreaseincoefficientofhorizontalsubgradereaction(kN/m4),seeequation (2.3.7) w1 :selfweightofdeepfoundationperunitofdepth(kN/m) α :constantdeterminedbybottomshape (α=1.0 for rectangular shapeandα=0.588 for round

shape) ppk :characteristicvalueofpassiveearthpressureatdepthh (m)(kN/m2),seePart II, Chapter 5,

1 Earth Pressure.Provided,howeverthathisgivenbyequation (2.3.19).

(2.3.13)

qud :designvalueofverticalbearingcapacityatbottomlevel(kN/m2),seeequation (2.3.2) γa :partialfactorforhorizontalresistanceforce

④WhenVerticalResultantForceattheBottomisoutsidetheCore12)Whentheverticalresultantforceactingatthebaseoffoundationisnotinsidethecore,atriangulardistributionofvertical subgrade reaction is assumedas shown inFig. 2.3.2 12).When thevertical subgrade reaction isexpressed as qd (kN/m2), themaximum subgrade reaction p1(kN/m2) in the front ground is obtained fromequation(2.3.14).

–438–


(2.3.14)

Thevalueofp1calculatedbyequation(2.3.14)shouldsatisfyequation(2.3.11).Inthiscase,h isobtainedbyequation(2.3.12).

(2.3.15)

where h :depthatwhichhorizontalsubgradereactionbecomesmaximum(m),seeFig. 2.3.2 W :selfweightoffoundation（kN） e :eccentricdistance（m）

Thedistancee isdefinedasshowninFig. 2.3.2.Whenthefoundationbottomisrectangularwiththelengthof2a (m)andthewidthof2b (m),thevalueofe iscalculatedbyequation(2.3.16).

(2.3.16)

In thecaseofaroundfoundationbottom, thecalculationmaybemadebyreplacing itwitharectangularfoundationbottomhavinglength2a andwidth2b definedbyequation(2.3.17).

(2.3.17)

where D :diameterofcircle(m)

Inthisway,thehorizontalbearingcapacitycanbeestimatedatasafersidebyapproximately10%.However,thissubstitutionshouldbeappliedonthebasisoftheappropriatejudgement,byreferringtoreference12).

N0

P0M0

kWW

2a

p

qud

qd

1

e

l

Fig. 2.3.2 When Resultant Force is Not Inside the Core


–439–

2.4 Pile Foundations2.4.1 General

(1)DefinitionofPileFoundationPilefoundationmeansafoundationwhichsupportssuperstructuresbymeansofasinglepileormultiplepiles,orafoundationwhichtransfersactionsonthefacilitiesorthefoundationtothegroundbymeansofsinglepilesormultiplepiles,evenwhennofacilitiesexistabovethepiles.

(2)DefinitionofPilePilemeans a columnar structural elementwhich is provided underground in order to transfer actions on thefacilitiesorthefoundationtotheground.

2.4.2 Fundamentals of Performance Verification of Piles

(1)Theloadsreceivedbypilesasaresultofactionsarecomplex.However,ingeneral,thecomponentsoftheloadsacting on a pile consist of the axial load component and the lateral load component, and verification can beperformedbasedonthepileresistanceperformancewithrespecttotheloadsintheserespectivedirections.

(2)Dependingonthetypesofsuperstructuressupportedbythepilefoundationandthetypesofloadsactingonthepiles,therearecasesinwhichisnecessarytoperformanalysisbythecomponentcouplingmethod,treatingthesuperstructureandpilefoundationascomponents.

2.4.3 Static Maximum Axial Pushing Resistance of Pile Foundations

[1] General

(1)The design value of the axial bearing resistance of pile foundations comprising vertical piles is generallydeterminedbasedonthemaximumaxialbearingresistanceduetotheresistanceofthegroundtoverticalsinglepilesasastandardvalueintakingconsiderationofthefollowingitems.

① Safetymarginfordisplacementintheaxialdirectionbasedongroundfailureanddeformationoftheground② Compressivestressofpilematerial③ Joints④ Slendernessratioofpiles⑤ Actionaspilegroup⑥ Negativeskinfriction⑦ Settlementofpilehead

(2)Theabove (1)describes thegeneralprinciple fordetermining theaxialbearing resistanceofpile foundationscomprisingverticalpiles.Inordertodeterminetheaxialbearingresistanceofapilefoundation,first,thestaticmaximumaxial bearing resistance due to the resistance of the ground is determined, and a safetymargin isconsideredonthis.Then,theaboveitems(a)to(g)areexamined,andthemaximumaxialbearingresistanceisreducedasnecessary.Theresultobtainedinthismanneristhedesignvalueoftheaxialbearingresistanceofthepileswhichshouldbeusedinperformanceverificationofthepilefoundation.

(3)Whenconsideringtheaxialbearingresistancecharacteristicsofasinglepilebasedontheresistanceoftheground,theaxialcompressiveloadP0actingonthepileheadofthesinglepileissupportedbytheendresistanceRpandtheshaftresistanceRfofthepile,andcanbeexpressedasinequation (2.4.1).

(2.4.1)where

Rt :axialbearingresistanceofsinglepile

(4)CharacteristicValueofAxialBearingResistanceofSinglePileDuetoResistanceofGround

① Typicalcharacteristicvaluesfortheaxialbearingresistanceofsinglepilesincludethefollowing.

(a) Second limit resistance:Resistance equivalent to the load at themaximum bearing resistance in a staticloadingtest.Provided,however,thatthedisplacementoftheendofthepileshallbewithinarangeofnomorethan10%oftheenddiameter.Thestaticmaximumaxialbearingresistancegivenbyappropriatecalculationsshallbeequivalenttothis.

(b)Firstlimitresistance:ResistanceequivalenttotheloadataclearbreakpointappearinginthelogP–logScurveinthestaticcompressiveloadingtest.PrepresentsloadattheheadandSmeanssettlementvalueattheheadofapile.

–440–


(c) Verticalspringconstantofpilehead:Slopeofthesecantofthepileheadloaddisplacementcurveinthestaticcompressiveloadingtest.

(5)SettingofDesignValueofAxialBearingResistanceofaSinglePileBasedonResistanceofGround

① Asafetymarginshallbeprovidedinthesecondlimitresistance.Thefollowingequationsareusedinthissafetymargin.Provided,however,thatγintheequationisthepartialfactorforitssubscript,andthesubscriptskanddindicatethecharacteristicvalueandthedesignvalue,respectively.

(2.4.2) (2.4.3)

where Rp :bearingresistanceoftheendofpile Rf :shaftresistanceofpileduringcompressiveloading

Incaseswhereonlythebearingresistanceofthepileheadcanbeobtainedintheloadingtest,andasafetymargincanbedeterminedfromthebearingresistanceofthepilehead,thefollowingequationcanbeused.

(2.4.4)where

Rt :axialbearingresistanceofsinglepile

ThestandardvaluesofthepartialfactorsγRiforthepileendresistance,theshaftresistance,andtheaxialbearingresistanceofpilesshallbeasshowninTable 2.4.1–Table 2.4.3.Provided,thatincaseswherepartialfactorsaredeterminedseparatelybycodecalibrations,etc.,inthedesignsystem.Thesubscriptirepresentsp,f,ort.

Table 2.4.1 Standard Values of Partial Factors for Shaft Resistance

Designsituation γRi:PartialfactorVariablesituationforloadactingduetoshipberthing 0.40Variablesituationforloadactingduetoshiptraction 0.40VariablesituationforLevel1earthquakegroundmotion 0.66Variablesituationforloadduringcraneoperation 0.40Variablesituationforloadactingduetowaves 0.66

Table 2.4.2 Standard Values of Partial factors for Pile End Resistance

Designsituation γRi:PartialfactorVariablesituationforloadactingduetoshipberthing 0.40Variablesituationforloadactingduetoshiptraction 0.40VariablesituationforLevel1earthquakegroundmotion 0.66(0.50)Variablesituationforloadduringcraneoperation 0.40Variablesituationforloadactingduetowaves 0.66(0.50)

Incasetheendofthepileremainsinanincompletebearingstratumwhichappearstobeunsafe,thefiguresinparenthesesshallbeused.

Table 2.4.3 Standard Values of Partial Factors for Total Resistance

Designsituation γRi:PartialfactorEndBearingpile* Frictionpile*

Variablesituationforloadactingduetoshipberthing 0.40 0.40Variablesituationforloadactingduetoshiptraction 0.40 0.40VariablesituationforLevel1earthquakegroundmotion 0.66 0.50Variablesituationforloadduringcraneoperation 0.40 0.40Variablesituationforloadactingduetowaves 0.66 0.50

*)Endbearingpilesandfrictionpilesshallbeasclassificationprovidedin(10).


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(6)Basedoninformationfortheperformanceverificationsofnormalportfacilities,theuseofthepartialfactorslistedabovemaygiveconservativeresults.

(7)Becausetheaxialbearingresistanceofpilesisstronglyaffectedbytheconstructionmethod,itisnecessarytocarryoutconstructioninadvancewithtestpilesandcollectinformationfortheverificationbyvarioustypesofexamination.Dependingontheresultsobtainedwiththetestpiles,itmaybenecessarytochangethedimensionsofthepilesortheconstructionmethod.

(8) Amongtheaxialresistancefactorsofacertainpile,whentheendresistanceofthepileRpisgoverning,thepileiscalledtheendbearingpile,andwhentheshaftresistanceRfisgoverning,itiscalledthefrictionpile.Accordingtothisdefinition,apilebecomesabearingpileorafrictionpiledependingonloadconditionssuchasthemagnitudeof the load, loadingvelocity, loadingduration, etc. Therefore, thedistinctionbetween endbearingpiles andfrictionpilescannotbeconsideredabsolute.Althoughthefollowingdefinitionslackstrictness,here,apilewhichpasses through soft ground andwhose end reaches bedrock or some other bearing stratum is called the endbearingpile,andapilewhoseendstopsinacomparativelysoftlayer,andnotahardlayerthatcouldparticularlybeconsideredabearingstratum,iscalledthefrictionpile.

(9) Ingeneral,whenapilepenetratestoaso-calledbearingstratumsuchasbedrock,ordensesandyground,axialresistanceislargerandsettlementissmallerthanwhenapileonlypenetratestoanintermediatelayer.Whenapilepenetratestoaso-calledbearingstratum,thepileitselfrarelysettles,evenwhenthesoftlayerssurroundingthepileundergoconsolidationsettlement.Therefore,negativeskinfrictionactsonthepile,applyingadownwardload,andtheamountofsettlementdiffersintheheadofthepileandthesurroundingground.Asthesephenomenacauseavarietyofproblems,cautionshouldbenecessary.Althoughthesedefectsareslightinpileswhichonlypenetratetointermediatelayers,settlementduetoconsolidationofthegroundunderthepilecontinues,andasaresult,thereisadangerofunevensettlement.

(10)Thepartialfactorfortheserviceabilitylimitisappliedtoultimatefailurephenomenaoftheground.Whenthedesignerdesirestoavoidyieldingoftheground,theuseofthefirstlimitresistanceisconceivable.ThePartialfactorinthiscasecanbesetatavalueontheorderof0.5.

(11)Incasepermanentdeformationofthegroundisexpectedtoremainafteranearthquake,separateexaminationisnecessary.Furthermore,becausetherearecasesinwhichtheshearstrengthofthesoilisremarkablyreducedbytheactionofgroundmotion,cautionisnecessary.Forexample,whensensitivecohesivesoilisaffectedbyviolentmotion,lossofstrengthisconceivable,andfrompastexamplesofearthquakedamage,ithasbeenpointedoutthatliquefactionmayoccurinloosesandylayersasaresultoftheactionofgroundmotion,causingalargedecreaseintheresistanceofpiles.Accordingly,withfrictionpiles,whichareeasilyaffectedbyphenomenaofthistype,duecautionisnecessaryinsettingthepartialfactors.

(12)Pile group means a group of piles in which the piles are mutually affected by pile axial resistance anddisplacement.

[2] Static Maximum Axial Resistance of Single Piles due to Resistance of Ground

(1)Thestaticmaximumaxialresistanceofsinglepilescanbeobtainedbyverticalloadingtestsorcalculationbystaticbearingcapacityformulasafteranappropriatesoilinvestigation.

(2)Asmethodsofestimatingthestaticmaximumaxialresistanceofsinglepilesfromtheresistanceoftheground,thefollowingareconceivable:

① Estimationbyloadingtests② Estimationbystaticbearingcapacityformulas③ Estimationfromtheexistingdata

(3)Itispreferabletoestimatethestaticmaximumaxialresistanceofsinglepilesfromtheresistanceofthegroundbyconductingaxialloadingtests.Determiningthecharacteristicvalueofthestaticmaximumaxialresistancebythismethodandthenconductingtheperformanceverificationisthemostrationalmethod.Inthiscase,thesoilconditionsmaydifferatthelocationwheretheloadingtestisconductedandatthesitewheretheactualpilesaretobedriven.Therefore,itisnecessarytoevaluatetheresultsofloadingtestswithcautionwithregardtotheirrelationshiptosoilconditions,basedonasoundunderstandingofthesoilconditionsatthelocationwheretheloadingtestisconducted.

(4)Itmaybedifficulttoconductloadingtestspriortotheperformanceverificationduetocircumstancesrelatedtotheconstructionperiodorcost.Insuchcases,estimationofthestaticmaximumaxialresistancedependingonthefailureofthegroundbystaticbearingcapacityformulastakingaccountoftheresultsofsoilinvestigationispermissible. Evenwhenestimating the staticmaximumaxial resistancebymethodsother than theabove-mentioned (2)(a), and conducting the performance verification by setting the axial resistance of piles based

–442–


thereon,theappropriatenessofthepileaxialresistanceusedintheperformanceverificationshouldbeconfirmedbyconductingloadingtestsattheinitialstageofconstruction.

[3] Estimation of Static Maximum Axial Resistance from Loading Tests

(1)Whenthesecondlimitresistancecanbeconfirmedfromtheload-settlementcurve,thecharacteristicvalueforstaticmaximumaxialresistancecanbesetbasedonthatvalue.Whenitisnotpossibletoconfirmthesecondlimitresistancefromtheload-settlementcurve,itispermissibletoconfirmthefirstlimitresistanceandusethatvalueasthecharacteristicvalue,ortoestimatethesecondlimitresistancefromthefirstlimitresistance.Itisalsopermissibletoobtaintheverticalspringcoefficientofthepileheadbasedontheload-settlementcurveatthepilehead.

(2)EffectofNegativeSkinFrictionWhenapilepassesthroughsoftground,thereisadangerthatthedirectionofskinfrictionmaybereversedduetoconsolidationofthesoftground,thisphenomenoniscallednegativeskinfriction.Insuchcases,itisnecessarytoconductteststoappropriatelyevaluatethepileendresistance.

(3)Load-totalSettlementCurveObtainedbyStaticLoadingTestAload-totalsettlementcurveobtainedbyastaticloadingtestisshownschematicallyinFig. 2.4.1.Thecurve,whichisinitiallygentle,showspronouncedbreakpoints,andthesettlementofthepileheadbecomesremarkable,eventhoughthereisnoincreaseintheload.

A

B

P1 P2P3

Load

Tota

l set

tlem

ent

Fig. 2.4.1 Yield Load and Ultimate Load

(4)CaseinwhichtheSecondLimitResistanceisnotObtainedDirectlybyLoadingTestAlthoughthereisnoproblemifthesecondlimitresistancecanbeobtainedbyaloadingtest,inmanycases,itisnotpossibletoapplyasufficientlylargeloadtoconfirmthesecondlimitresistanceduetoconstraintsrelatedtothetestequipment.Insuchcases,thesecondlimitresistancecanbeassumedbymultiplyingthefirstlimitresistanceobtainedbyaloadingtestby1.2.ThisjudgmentisbasedontheresultsofresearchbyYamakataandNagai14)onsteelpipepilesandstatisticalstudiesbyKitajimaetal.15)Whenthefirstlimitresistancealsocannotbeobtainedinloadingtests,thesecondlimitresistanceshouldbeassumedtobe1.2timesthemaximumloadinthetest,oramethodofsettingthedesignvalueofthepileaxialresistancewhichdoesnotdependonthesecondlimitresistanceshouldbeexamined.Ineithercase,aconditionwhichassumesthatthepileaxialresistanceestimatedinthiswaywillbelargerthanthepileaxialresistancethatcanactuallybeexpectedisrequired.

(5)AlternativeLoadingTestMethodsforStaticLoadingTest

① Therapidloadtest17)isaloadingtestwhichshallbeperformedinlessthan1second.Testequipmentcapableofapplyingalargeinstantaneousloadisnecessary;however,becausevariousinnovationshaveeliminatedtheneedforreactionpiles,thetestcanbeperformedmoreeasilythanthestaticloadingtest.

② Theendloadingtestisamethodinwhichajackisinstallednearthebottomendofthepile,andthepilebodyispushedupwhilepushingthebottomendofthepile.Thismethodenablesseparatemeasurementofthepileendresistanceandpileshaftresistance.


–443–

③ Thedynamicloadingtest18)isatypeofloadingtestwhichemploysanordinarypiledriver.Asafeatureofthistestmethod,changesovertimeintheelasticstrainanddisplacementofthepileheadaremeasured.Inthistest,therearelimitstotheresistancewhichcanbeobtained,dependingonthemagnitudeofthepile-drivingenergy.Therefore,whentheaxialresistancewhichistobeestimatedislarge,asinlongorlarge-diameterpiles,inmanycasesitisnotappliedasamethodfordirectestimationofthesecondlimitresistance.Itcanbeusedtoestimatetherelationshipbetweenstaticresistanceanddrivingstopcontrolduringconstruction.

[4] Estimation of Static Maximum Axial Resistance by Static Resistance Formulas

(1)Whenestimatingstaticmaximumaxialresistanceusingstaticresistanceformulas,attentionmustbepaidtothesoilconditions,pileconditions,constructionmethods,andlimitsofapplicabilityofthestaticresistanceformulas.

(2)Thestaticmaximumaxialresistanceobtainedbystaticresistanceformulasmaybeconsideredtobeequivalenttothesecondlimitresistance.

(3)Whenusingstaticresistanceformulas,itisnecessarytoconsiderdifferencesinconstructionmethods.

① Pilesdrivenbyhammerdrivingmethoda)

(a)Whenemployingstaticresistanceformulasusingtheresultsofstandardpenetrationtestresultsandundrainedshearstrengthofground

i) Endresistanceofapile

a) Equation(2.4.5)canbeusedinestimatingendresistanceofapilewhenthebearingstratumissandyground.

(2.4.5)where

RPk :characteristicvalueofendresistanceofapilebystaticresistanceformula(kN) Ap :effectiveareaofendofpile(m2).Indeterminingtheeffectiveareaofanopen-endedpile,itis

necessarytoconsiderthedegreeofclosureoftheendofthepile. N :Nvalueofgroundaroundpileend

Provided,however,Niscalculatedbyequation(2.4.6).

(2.4.6)where

N1 :N-valueatendofpile(N1≤50)

N2 :meanN-valueinrangeabovetheendofpiletodistanceof4B (N2 ≤50) B :diameterorwidthofpile(m)

Inequation (2.4.5),thecoefficientoftheequationproposedbyMeyerhofbasedonthecorrelationbetweenthestaticpenetrationtestandthestandardpenetrationtestinsandygroundwasmodifiedtoconformtorealconditions. InestimatingtheultimatepileendresistanceofpilessupportedbygroundwithanN-valueof50ormore,cautionisnecessary,asN-valuesitselfisnotreliablewhenitismeasuredlargerthan50,andfurthermore,theapplicabilityofequation (2.4.5)initscurrentformtohardgroundofthiskindhasnotbeenadequatelyconfirmed.

b)Inestimationofthepointresistanceofpileswhenthepointofthepilepenetratesclayeyground,equation(2.4.7)canbeused.

(2.4.7)where

cp :undrainedshearstrengthatpositionoftheendofapile(kN/m2)

Thebearingcapacitycoefficientoftheendresistanceofapileincohesivesoilgroundshowninequation(2.4.7)wasobtainedbythesamemethodasthebearingcapacityoffoundationsoncohesivesoilgroundin2.2 Shallow Spread Foundations.Becausethecross-sectionalshapeofordinarypileshaspointsymmetry,B/L=1.0,andBk/cp <0.1.Basedonthesefacts,thebearingcapacitycoefficientNc offoundationsisobtainedfromFig. 2.2.2, see2.2.3 Bearing Capacity of Foundations on Cohesive Soil Ground. Therefore, thebearingcapacitycoefficientoftheendofthepileis6.Accordingly,theendresistanceRpofthepilecanbeshownas6cpAp.

–444–


As the undrained shear strength used here, the undrained shear strength cu obtained in the unconfinedcompressiontestwascommonlyuseduptothepresent.

ii) PileshaftresistancePileshaftresistancemaybeobtainedasthesumoftheproductsobtainedbymultiplyingtheaveragestrengthofskinfrictionperunitofareaineachlayerwithwhichthepileisincontact.Namely,equation(2.4.8)canbeused.

(2.4.8)where

Rfk :characteristicvalueofpileshaftresistance(kN)

rfki :averagestrengthofskinfrictionperunitofareaini-th layer(kN/m2)

Asi :circumferentialareaofpileincontactwithgroundini-thlayer(=lengthofoutercircumferenceUsxthicknessoflayerl)(m2)

Forsandyground,equation (2.4.9)canbeused.

(2.4.9)where

N :meanN-valueofi-thlayer

Forcohesivesoilground,equation(2.4.10)canbeused.

(2.4.10)where

:meanadhesionofpileini-thlayer(kN/m2)

Here,thevalueoftheadhesionofthepilemaybeobtainedasfollows.incase c ≤100kN/m2;ca=cincase c >100kN/m2;ca=100kN/m2 (2.4.11)

However,becausetheoreticalproblems24)ariseinobtainingtheadhesionofpilesfromtheundrainedshearstrengthcoftheground,thevalueofadhesionshouldbeexamined,payingdueattentiontothecharacteristicsofthegroundandconditionsofthepiles.

(b)Methodofestimatingtheendresistanceofpileswhichremaininsandygroundfrombearingcapacitytheory

i) ExpansionofbearingcapacitytheoryofshallowspreadfoundationsIftheshearresistanceangleofthebearingstratumisknown,theendresistanceofthepilecanbeestimatedasanexpansionofthebearingcapacitytheoryforshallowspreadfoundations.Here,thefollowingmethodisintroducedasanexample.Theendresistanceofthepileisobtainedusingequation (2.4.12).

(2.4.12)where

Nq :bearingcapacitycoefficientproposedbyBerezantzev,seeFig. 2.4.2σ’v0 :effectiveoverburdenpressureattheendofpile(kN/m2)

WhenNq is tobeobtainedfromFig. 2.4.2, it isnecessary toobtain theshear resistanceangle. Whenobtainingtheshearresistanceangle,equation(2.3.21)inPart II, Chapter 3, 2.3.4 Interpretation Methods for N Valuescanbeused.Whentheshearresistanceangleistobeobtainedbyatriaxialcompressiontest,itisnecessarytoconsiderthefactthattheshearresistanceangleisreducedasaresultofconfiningpressure.


–445–

0

50

100

150

20 25 30 35 40 45

Shear resistance angle (º)

Bea

ring

capa

city

coe

ffic

ient

Nq

Fig. 2.4.2 Bearing Capacity Coefficient proposed by Berezantzev

ii) VoidexpantiontheoryThefailuremodewhentheareaaroundtheendofthepilefailsduetocompressiveforceisconsideredtobeoneinwhichaplasticregionformsattheoutsideofasphericalrigidregionaroundtheendofthepileandisinbalancewithanelasticregionatitsouterside.25)Thistheoryiscalledthevoidexpantiontheory. End resistance of a pile according to the void expantion theory can be shown by the followingequations.26),27)

(2.4.13)

where qp :endresistanceofapileperunitarea(kN/m2) Irr :correctedrigidityindex Ir :rigidityindexφcv’ :shearresistanceangleinlimitcondition;assumesφcv′=30+Δφ1+Δφ2.thevaluesofΔφ1andΔφ2

shallbeasshowninTable 2.4.4. Δav :coefficientdefiningcompressibilityofground.Δav =50(Ir)−1.8 G :shearrigidity.MaybeobtainedasG=7000N0.72(kN/m2).NistheN-valuearoundtheendof

thepile.

Table 2.4.4 ∆φ1; ∆φ2 of Sand and Gravel

(Dependsonparticleshape) ∆φ1(°) (Uniformitycoefficient) ∆φ2(°)Round 0 Uniform(Uc<2) 0

Somewhatangular 2 Moderateparticlesizedistribution(2<Uc<6) 2Angular 4 Goodparticlesizedistribution(6<Uc) 4

–446–


0 5 10 15 20 25 30

0

20

40

60

80

Measured300NVoid Expantion theory

End bearing capacity of pile per unit area (MN/m2)

Dep

th a

t the

end

of p

ile, GL

(m)

Pile diameter ≤1000mm

Fig. 2.4.3 Comparison of Measured End Bearing Capacity of Pile and Results of Calculation by Void Expantion Theory

Fig. 2.4.3showstheresultsofacomparisonofthemeasuredendbearingcapacityofpileandtheresultsofanestimationofendbearingcapacitybytheexpandedvoidtheoryassumingφcv′=34.

② Thevibratorypiledrivingmethod,vibro-hammermethod,isincreasinglybeingusedfordrivingpilesbecauseofthecapacityincreaseofpile-drivingmachineryinrecentyears.Astheprinciplesofthismethoddifferfromthoseofpiledrivingbyhammer,thebearingcapacityshouldbecarefullyestimated.Whenusingthismethod,thegroundshouldbecompactedbythemethodofhammerpiledrivinginsteadofvibratorypiledrivinginthecourseoffinaldriving,orverticalloadingtestsshouldbeconductedtoconfirmthecharacteristicsofbearingcapacityofthegroundinquestion.

③ Inrecentyears,theuseofpileinstallationmethodbyinnerexcavationinsteadofpiledrivingbyhammerhasbeenincreasinginportandharborconstructionworks.Insuchcases,thecharacteristicsofthebearingcapacityofpilesinquestionshouldbeconfirmedbyverticalloadingtests.

(4) EffectiveAreasofPileEnd

① Evenifthereisnoshoeonthepileend,theendbearingareaofsteelpilescanbeconsideredclosed,asshownbytheshadedareasinFig. 2.4.4.Inthiscase,theouteredgeoftheclosedareaistakenastheperimeter.Thisisbasedonthefollowingprinciple.SoilenterstheinteriorofsteelpipesorthespacebetweentheflangesofH-shapedsteelduringthepiledrivinguntiltheinternalfrictionbetweenthesoilandthesurfaceofsteelpilebecomesequaltotheendresistanceofpile.Thisbalancepreventssoilfromenteringtothepilesandhasthesameeffectasthecasewhentheopenendsectionisclosed.Butcompleteclosurecannotbeexpectedinthecaseoflarge-diameterpiles.Insuchcasesthepluggingratioshouldbeexamined.

Fig. 2.4.4 End Bearing Area of Steel Piles

② PluggingratioThemechanismoftheendresistanceofopenendedpilesiscomposedofthesumoftheendresistanceofthesubstantialpartoftheendofthepileandtheskinfrictionoftheinnersurfaceofthepileasshowninFig. 2.4.5.


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Theresistancefromtheinnersurfaceofthepileisconsideredtobedeterminedfromthedirectstressactiononthecircumferenceandtheinnercircularareaofthepile.Becausethepilecross-sectionalareaisproportionaltothesquareofitsdiameteranditscircumferenceisproportionaltoitsdiameter,asthediameterofapilebecomeslarger,theconceptthatthetotalcross-sectionalareaofthepileiseffectiveforresistancelosesvalidity.Inpilesofthis type,amongtheresistanceswhichareconceivableduetoclosureofthepileend,onlysomefractioncanbeexpectedtofunctionastheendresistance.Thatfractioniscalledthepluggingeffectratio.Thesizeofthepluggingeffectratioisaffectedbythediameterorwidthofthepile,thepenetrationdepthofthepile,thepropertiesoftheground,theconstructionmethod,andcannotbedeterminedsimplybythediameterorwidthofthepilealone.

Pu

Rp Rp

t

RfRf Rf

d

Pu : actionsRf : outer skin friction of pileRp : resistance attributable to wall thickness of pile end in open-ended pileRf : resistance due to plugged soild : ile diameter

Fig. 2.4.5 Schematic Diagram of Plugging Effect Ratio

③ Differentfrompluggingeffectratio,thepluggingratioreferstotheratiooftheendresistancethatcanactuallybeexpectedtotheendresistanceobtainedbystaticresistanceformulas.Frompastdata,thepluggingratiocanbeconsideredtobe100%whenthediameterofsteelpipepilesislessthan60cmorH-shapedsteelpileswhichshortsidewidthislessthan40cm.Numeroustheoreticalcalculationmethods30),31),32),33),34),35)andresultsoflaboratoryexperiments36),37)havebeenpresentedasmethodsofestimatingthepluggingeffectratiowhichconsiderthevariousfactorsmentionedaboveforpileswithlargerdiametersorwidths.Therearealsoexamplesofstudybyactuallyconductingpileloadingtests.However,inadditiontothefactthatthepluggingeffectratiovariesgreatlydependingonthepropertiesoftheground,theconstructionmethod,andotherfactors,thestateofpluggingofactualpilesdiffersdependingonthepenetrationdepth,includingthestressintheground,makingitdifficulttoobtaintheratiobytheoreticalcalculation.

④ TheJapanAssociationofSteelPipePilescollectedexamplesofmeasurementsof thepluggingratio.38)Fig. 2.4.6shows databasedthereontogetherwithadditionalnewdata.Thenewdataaddedhereareforpileswithdiametersof1100mmto2000mm. According to thesedata, thepluggingratio for thecasewhereequation(2.4.5)isconsideredtoexpresstheendresistanceforcompletepluggingisintherangeof30-140%.Inanycase,itappearsthatthereisvirtuallynocorrelationbetweentheembeddedlengthratiointhebearingstratumandthepluggingratio.Provided,however,thatthereisclearlyadifferenceinthepluggingratioinsteelpipepileswithdiametersoflessthan1000mmandthosewithdiametersgreaterthan1000mm.Cautionisparticularlynecessarywhenusinglargediametersteelpipepileswithdiameterslargerthan1000mm.Fig. 2.4.7showstheresultswhenthex-axisindicatesthepilediameter.Inspiteofsomedispersioninthedata,thepilediameterhasalargeeffectonthepluggingratio,ascanbeunderstoodbycomparisonwithFig. 2.4.6. Thepluggingratioisaffectedbyconstructionmethodsandsoilcondition,thereforeitisnecessarytograspthepluggingratioinactualconstructionworksandbycarryingouttheloadingtests.

–448–


0

0.5

1

1.5

0 2 4 6 8 10 12

OD ≤ 650mmOD 700~900mmOD ≥ 1000mm

penetration length ratio in bearing stratum L/D

*

* ) Thin stratum bearing pile

End

resi

stan

ce o

f pile

bas

ed o

n lo

adin

g te

st /

(300NAp

)

Fig. 2.4.6 Plugging Effect of Open Ended Piles (effect of embedded length ratio in bearing stratum)

0

0.5

1

1.5

0.5 1 1.5 2

Mea

sure

d va

lue

/ (30

0NAp

)

Pile diameter (m)

Fig. 2.4.7 Plugging Effect of Open Ended Piles (effect of pile diameter)

(5) BearingCapacityofSoftRockWhenpilesaresupportedonsoftrockorhardclay,thebearingcapacitymaybecalculatedbyequation(2.4.5).Ifunconfinedcompressivestrengthqu (kN/m2)hasbeenmeasuredbyundisturbedsoilsamples,equation(2.4.14)mayalternativelybeused.

(2.4.14)

Further,thevalueofqu shouldbereducedto1/2or1/3ofthemeasurementvaluesdependingontheconditionsofcrackingintheground.Inanyevent,however,thevalueofqu shouldnotexceed2×104kN/m2.


–449–

DN

DN

N=2 N=4 N=9

N ; Division Number

[5] Examination of Compressive Stress of Pile Material

Whendeterminingtheaxialresistanceofpiles,itisnecessarytoconsidersafetywithrespecttofailureofthepilematerial.

[6] Decrease of Bearing Capacity due to Joints

(1) Ifitisnecessarytosplicepiles,thesplicingworkshallbeexecutedunderappropriatesupervisionandreliabilityofjointsofsplicedpileshallbeconfirmedbyappropriateinspection.

(2)Ifjointsaresufficientlyreliable,itmaynotbenecessarytodecreasetheaxialbearingcapacityduetojoints.

(3)Whensplicedpilesareused,thejointssometimesbecometheweakpointsinthepile.Therefore,itisnecessarytoadequatelyexaminethestructuralreliabilityofthejoints.Ifthestructuralreliabilityofthejointsisinadequate,itisnecessarytoreducetheaxialresistance,inconsiderationoftheeffectofthejointonthebearingcapacityofthepilefoundationasawhole.

(4)In-sitecircularweldingbysemi-automaticmethodsisgenerallyemployedforthesplicingofsteelpipepilesusedinthefieldofportandharborconstructionworks.Whensuchhighlyreliablejointingmethodsareappliedunderappropriatesupervisionandthereliabilityofthejointshasbeenconfirmedbyinspection,itisnotnecessarytodecreasetheaxialbearingcapacity.

(5)Forothermattersrelatedtothestructuresofjoints,2.4.6[4] Joints of pilesofpilescanbeusedasreference.

[7] Decrease of Bearing Capacity due to Slenderness Ratio

(1)Forpileswithaverylargeratiooflengthtodiameter,theaxialbearingcapacityofpilesneedstobedecreasedinconsiderationoftheaccuracyofinstallation,unlessthesafetyofbearingcapacityisconfirmedbyloadingtests.

(2)This provision takes account of the fact that the inclination of piles during installation reduces their bearingcapacity.Ifloadingtestsareconductedonfoundationpiles,theultimatebearingcapacitycanbedetermined,accountingforthedecreaseofbearingcapacityduetoinstallationaccuracy.Therefore,inthiscasethedecreaseduetotheslendernessratiomaynotnecessarilybetakenintoaccount.

(3)When decreasing the bearing capacity due to the slenderness of piles, the following valuesmay be used asreferences:

① Exceptforsteelpipepiles

(2.4.15)

② Forsteelpiles

(2.4.16)

–450–


where α :rateofreduction(%) :pilelength(m) d :pilediameter(m)

[8] Bearing Capacity of Pile Groups

(1)Whenagroupofpilesareexaminedasapilegroup,thebearingcapacityofpilegroupmaybestudiedasasingleanddeepfoundationformedwiththeenvelopesurfacesurroundingtheoutermostpilesinthegroupofpiles.

(2)TerzaghiandPeckstatethatafailureofapilegroupfoundationdoesnotmeanthefailureoftheindividualpilesbutfailureasasingleblock,45),46)basedontheprinciplethatthesoilandpilesinsidethehatchedareainFig. 2.4.8 workasasingleunitwhentheintervalsbetweenthepilesaresmall.Theaxialresistanceofapilegroupwhenconsideredinthismannerisexpressedbyequation(2.4.17).

(2.4.17)

where Rgud :designvalueofaxialresistanceofpilegroupassingleblock(kN) qdk :staticmaximumaxialresistance(characteristicvalue)whenbottomofblockisassumedtobe

foundationloadplaneaccordingtoTerzghi’sequation(kN/m2) γq :partialfactorforbottombearingcapacity(bearingcapacityoffoundationonsandygroundand

bearingcapacityoffoundationoncohesivesoilgroundin2.2 Shallow Spread Foundations) Ag :bottomareaofpilegroup(m2) U :perimeterlengthofpilegroup(m) L :penetrationlengthofpiles(m)

sk :meanshearstrengthofsoilincontactwithpiles(characteristicvalue)(kN/m2) γs :partialfactorforskinfriction(see2.4.3[1] General)

Theaxialresistanceperpileisshownbyequation(2.4.18).

(2.4.18)where

Rad :designvalueofaxialresistanceperpileagainstfailureasablock(kN) γ’2 :meanunitweightofwholeblockincludingpilesandsoil(kN/m3);belowgroundwaterlevel,the

meanunitweightiscalculatedconsideringbuoyancy,andabovegroundwaterlevel,usingthewetunitweight.

n :numberofpilesinpilegroup

Inthecaseofcohesivesoil,equation (2.4.18) isreplacedbyequation(2.4.19),wherec isundrainedshearstrengthandγ’2 ≒γ2 (γ2:meanunitweightofsoilabovetheendofthepile).

(2.4.19)

where B :shortsidewidthofpilegroup(block)(m) B1 :longsidewidthofpilegroup(block)(m) γa :partialfactor(see2.2.3 Bearing Capacity of Foundations on Cohesive Soil Ground)

As the axial resistance of each pilewhen used as a pile group, it is necessary to use the smaller of theaxialresistanceofthesinglepilesortheresistanceagainstblockfailuregivenbyequation (2.4.18)or(2.4.19),respectively.


–451–

Perimeter length U

sL

Fig. 2.4.8 Pile Group Foundation

[9] Examination of Negative Skin Friction

(1) If bearing piles penetrate through a soil layer that is susceptible to consolidation, it is necessary to considernegativeskinfrictionwhencalculatingtheallowableaxialbearingcapacityofpiles.

(2)Whenapilepenetratesthroughacohesivesoftlayertoreachabearingstratum,thefrictionforcefromthesoftlayeractsupwardsandbearsapartoftheloadactingonthepilehead.Whenthecohesivesoftlayerisconsolidated,thepileitselfissupportedbythebearingstratumandhardlysettles,thedirectionofthefrictionforceisreversed,asshowninFig. 2.4.9.Thefrictionforceonthepilecircumferencenowceasestoresisttheloadactingonthepilehead,butinsteadturnsintoaloaddownwardsandplacesalargeburdenontheendofthepile.Thisfrictionforceactingdownwardsonthepilecircumferenceiscalledthenegativeskinfrictionornegativefriction.

(a) (b)

Weak layer

Bearing stratum

Consolidationsettlement

Neg

ativ

e sk

in fr

ictio

n

Posi

tive

skin

fric

tion

Fig. 2.4.9 Negative Skin Friction

(3)Althoughtheactualvalueofnegativeskinfrictionisnotwellknownyet,themaximumvaluemaybeobtainedfromequation(2.4.20).

(2.4.20)

where Rnf,maxk : characteristicvalueofnegativeskinfrictionforsinglepile(maximumvalue)(kN)

–452–


φ : circumferenceofpiles(perimeterofclosedareainthecaseofH-shapedsteelpiles)(m) L2 : lengthofpilesintheconsolidatinglayer(m)

fs : meanskinfrictionintensityintheconsolidatinglayer(kN/m2)

(4)Intheabove, fs incohesivesoilgroundissometimestakenatqu/2.Ifasandlayerislocatedbetweenconsolidatinglayers,orifasandlayerliesontopofconsolidatinglayer,thethicknessofthesandlayershouldbeincludedinL2.Theskinfrictioninthesandlayerissometimestakenintoaccountfor sf .Thecharacteristicvalueofnegativeskinfrictioninsuchcasesisshownbyequation(2.4.21).

(2.4.21)

where Ls2 : thicknessofsandlayerincludedinL2(m) Lc : thicknessofcohesivesoillayerincludedinL2(m)

Ls2+Lc=L2

Ns2 : meanSPT-N-valueofthesandlayerofthicknessLs2 qu : meanunconfinedcompressivestrengthofcohesivesoillayerofthicknessLc (kN/m2)

(5)Inpilegroups,thecharacteristicvalueofnegativeskinfrictionmaybecalculatedbyobtainingthenegativeskinfrictionassumingallofthepilesformasingleanddeepfoundation,anddividingtheresultbythenumberofpilestoobtainthenegativeskinfrictionperpile.(seeFig. 2.4.10).

(2.4.22)where

Rnf, maxk : characteristicvalueofnegativeskinfrictionforpilegroup(kN) U : perimeterlengthofgroupofpilesactingaspilegroup(m) H : depthfromgroundleveltobottomofconsolidationlayer(m) s : meanshearstrengthofsoilinrangeofH inFig. 2.4.10 (kN/m2) Ag : bottomareaofgroupofpilesactingaspilegroup(m2) γ : meanunitweightofsoilinrangeofL2inFig. 2.4.10 (kN/m3) n : numberofpilesingroupofpilesactingaspilegroup

Equations (2.4.20) to(2.4.22)givetheconceivablemaximumvaluefornegativeskinfriction. Theactualvalueofnegativeskinfrictionisconsideredtobegovernedbytheamountofconsolidationsettlementandthespeed of consolidation, the creep characteristics of the soft layers and the deformation characteristics of thebearingstratum.

Con

solid

atio

n la

yer

H L2

Fig. 2.4.10 Skin Friction of Pile Group

(6)Thedesignvalueofnegativeskinfrictioncanbecalculatedbythefollowingequation,usingthecharacteristicvalueofnegativeskinfriction.

(2.4.23)where

γnf : partialfactorfornegativeskinfriction(normally,1.0canbeused)


–453–

(7)VerificationWhencalculatingtheaxialbearingcapacityofpiles,manyuncertaintiesexistastohowtheinfluenceofnegativeskin friction should be considered. However, at the present stage,when negative skin friction is adequatelyconsidered, onemethodassumes safetywhen it is confirmed that the force transmitted to the endof thepilepossessesadequatesafetyagainstfailureofthegroundatthepileendandcompressivefailureofthepilematerialcrosssection.Thatis,whenthedesignvalueoftheaxialbearingcapacityintheserviceabilitylimitstateisRad,inadditiontosecuringtherequiredsafetyagainstordinaryloads,Radsatisfiesequations (2.4.24)and(2.4.25).

(2.4.24)

(2.4.25)where

Rad : designvalueofaxialbearingcapacity(serviceabilitylimitstate)(kN) Rpk : characteristicvalueofendresistanceofpile(secondlimitresistance)(kN)

Rnf,maxd : designvalueofmaximumnegativeskinfriction(kN) (smallerofvaluesforsinglepileorpilegroup) σfk : characteristicvalueofcompressiveyieldstressofpile(kN/m2) Ae : effectivecross-sectionalareaofpile(m2) γRp : partialfactorforendresistanceofpile(generally,0.8canbeused) γσf : partialfactorforcompressiveyieldstressofpile(generally,1.0canbeused)

ThecharacteristicvalueforendresistanceofpileRpk canbecalculatedusingequation (2.4.5). Whenthepilepenetratesintothebearingstratum,thecircumferenceresistanceofthatsectionshallbeincludedinthepileendbearingcapacity.Inthiscase,thecharacteristicvalueofendresistancecanbecalculatedusingthefollowingequation(seeFig. 2.4.11).

(2.4.26)where

Rpk : characteristicvalueofendbearingcapacityofpile(ultimatevalue)(kN) N : N-valueofgroundattheendofpile Ap : areaoftheendofpile(m2)

Ls1=L1 : lengthofpilepenetratesintobearingstratum(sandyground)(m) Ns1 : meanN-valueforzoneLs1 φ : circumferenceofpile(m)

L2

L1=Ls1 Bearing ground

Fig. 2.4.11 End Bearing Capacity

–454–


[10] Examination of Pile Settlement

Theaxialbearingcapacityofpileshallbedeterminedinsuchawaythatanestimatedsettlementofpileheaddoesnotexceedtheallowablesettlementdeterminedforsuperstructures.

2.4.4 Static Maximum Pulling Resistance of Pile Foundations

[1] General

(1)Thedesignvalueofthepullingresistanceoffoundationpilesmustbedeterminedconsideringthefollowingitems,usingthestaticmaximumpullingresistanceofasinglepileduetofailureofthegroundasastandard.

① Tensilestressofpilematerial② Effectofpilejoints③ Loadonpilegroupduetoactions④ Upwarddisplacementofpilesbypulling

(2)Thedesignvalueofthepullingresistanceofpilescanbeobtainedasfollows.First,thecharacteristicvalueofthestaticmaximumpullingresistanceofasinglepileisobtainedbasedonfailureofthegroundandaddingsafetymargin.Thedesignvalueofthepullingresistanceofthepileisthendeterminedconsideringthestressofthepilematerial,actionsofjoints,thepilegroupanddisplacement..

(3)Thecharacteristicvaluesofthepullingresistanceofpilesareasfollows;

① ThefirstlimitresistanceThefirstlimitresistanceistheloadwhentheshearingstressgeneratedinthepilecircumferenceorthesoilsurroundingthepilebypullingofthepileaffectssubstantiallytheentirelengthofthepileandyieldingbegins.WhenaloadingtestisperformedandthelogP–logScurveisdrawn,theclearbreakpointwhichappearsonthecurveshallbeconsideredasthefirstlimitresistance.

② ThesecondlimitresistanceThesecondlimitresistanceis theresistancewhenthepullingresistanceof thepilecircumferenceshowsitsmaximumvalue.Ifthemaximumresistanceisunclear,thesecondlimitresistanceshallbetheloadwhenthedisplacementoftheendofthepilereaches10%ofthediameterorwidthofthepileend.Theresistanceobtainedusingstaticbearingcapacityformulasmaybeconsideredequivalenttothisresistance.

Maximum pulling force

Pulling force

Dea

dwei

ght

Dis

plac

emen

t

Fig. 2.4.12 Pulling Resistance of Piles

(4)SettingofDesignValueofPullingResistanceofSinglePile

(a)Asafetymarginshallbetakeninthesecondlimitresistance.Asthemethod,thefollowingequationcanbeused.

(2.4.27)where

γR : partialfactor

ThestandardvalueofpartialfactorscanbeasshowninTable 2.4.5.Table 2.4.5 Standard Values of Partial Factors for Total Resistance


–455–

Designsituation γR:PartialfactorVariablesituationforloadactingduetoshipberthing 0.33Variablesituationforloadactingduetoshiptraction 0.33VariablesituationforLevel1earthquakegroundmotion 0.40Variablesituationforloadduringcraneoperation 0.33Variablesituationforloadactingduetowaves 0.40

(5)Incaseswherethereappearstobeapossibilityofliquefactionofsandylayersduringanearthquake,itisnecessarytodeterminepullingresistancegivingdueconsiderationtothisfact.

(6)Becausetheselfweightofthepilecanbeexpectedtoactreliablyaspullingresistancetogetherwiththeweightofthesoilinthepile,apartialfactorof1.0maybeusedforthis.Accordingly,itisrationaltocalculatethedesignvalueofthepullingresistanceduetofailureofthegroundfromthecharacteristicvalueofpullingresistanceduetofailureofthegroundasfollows.Provided,however,thatwhentheselfweightofthepileiscomparativelysmall,thisprocessisnormallyomitted.Whenthediameterofthepileisexcessivelylarge,itisconsideredthatthesoilfilledinthepileisnotnecessarilyliftedwiththepile,butseparatesandfallsdown.

① whenmaximumpullingresistanceisobtainedbypullingtest

(2.4.28)

② whenmaximumpullingresistanceisobtainedbystaticbearingcapacityformula

(2.4.29)where

Rad : designvalueofallowablepullingresistanceofpile(kN) Wpk : characteristicvalueofselfweightofpilewithbuoyancysubtracted(kN) Rut1k : characteristicvalueofmaximumpullingresistanceofpilebypullingtest(kN) Rut2k : characteristicvalueofmaximumpullingresistanceofpilebystaticbearingcapacityformula (kN) γ : Partialfactorcorrespondingtosubscript

[2] Static Maximum Pulling Resistance of Single Pile

(1) Itispreferabletoobtainthemaximumpullingresistanceofasinglepileonthebasisoftheresultsofpullingtests.

(2)Unlikeaxialbearingcapacity,therearefewcomparativedataforpullingresistance,andindirectestimationsmayinvolvesomerisk.Thusconductofpullingtestsispreferabletodeterminethemaximumpullingresistanceofasinglepile.However,inthecaseofrelativelysoftcohesivesoil,skinfrictionduringdrivingofapileisconsideredto be virtually the same as that during pulling of piles. Therefore, themaximumpulling resistancemay beestimatedfromtheresultsofloadingtests(pushingdirection)andstaticbearingcapacityequations.

(3)Estimationofthemaximumpullingresistancebystaticbearingcapacityformulasmayfollowtheexplanationgivenin2.4.3[4]. Estimation of Static Maximum Axial Resistance by Static Resistance Formulas.However,theendbearingcapacityshallbeignored.Thus,forpilesdrivenbyhammer,thefollowingequationsmaybeused.

① Sandyground

(2.4.30)

② Cohesivesoilground

(2.4.31)where

Rutk : characteristicvalueofthemaximumpullingresistanceofpile(kN) N : meanN-valuefortotalpenetrationlengthofpile As : totalcircumferenceareaofpile(m2)

ca : meanadhesionfortotalpenetrationlengthofpile(kN/m2)

(4)Incaseswherethestaticmaximumpullingresistanceofapileistobeestimatedusingastaticbearingcapacityformula,examinationissometimesperformedusingTerzaghi’sequation,whichisshowninequation (2.4.32).

–456–


Inthiscase,anappropriatevalueshallbeadopted,basedoncomparisonofthevaluescalculatedusingequation (2.4.30)and equation (2.4.31)andthevaluecalculatedusingTerzaghi’sequation.

(2.4.32)

(2.4.33)where

Rutk : characteristicvalueofthestaticmaximumpullingresistanceofpile(kN) Rfk : characteristicvalueofskinfrictionofpile(kN) φ : circumferenceofpile(m) L : penetrationdepthofpile(m)

fsk : characteristicvalueofaveragestrengthofskinfriction(kN/m2)

caik : characteristicvalueofadhesionbetweensoilandpileini-thlayer(kN/m2) Ksk : characteristicvalueofcoefficientofhorizontalearthpressureactingonpile qik : characteristicvalueofmeaneffectiveoverburdenpressureini-thlayer(kN/m2) μk : characteristicvalueofcoefficientoffrictionbetweenpileandsoil li : thicknessofi-thlayer(m)

For ca and μ, see 2.4.3[4] Estimation of Static Maximum Axial Resistance by Static Resistance Formulas. ThevalueofthecoefficientofhorizontalearthpressureKs isconsideredtobesmallerthaninthecaseofpushing. Ingeneral,avaluebetween0.3and0.7,whichisclose to thecoefficientofearthpressureatrest, isfrequentlyused.

[3] Items to be Considered when Calculating Design Value of Pulling Resistance of Piles

(1)Whendeterminingthepullingresistanceofpiles,itisnecessarytoconsiderthefollowingitems.

① Theresistanceusedinverificationofthepullingresistanceofpilesshouldbenomorethantheproductoftheresistanceofthepilematerialandtheeffectivecross-sectionalareaofthepile.

② Insplicedpiles,thepullingresistanceofthepilebelowthejointisgenerallyignored.Provided,however,thatwhenhigh-qualityjointscanbeusedinsteelpiles,thepullingresistanceofthelowerpilecanbeconsideredwithintherangeofthetensilestrengthofthejointafterconfirmingthereliabilityofthejoint.

③ Incaseofapilegroup,itisnecessarytoexaminethepullingresistanceasasingleblocksurroundedwiththeenvelopesurfaceoftheoutermostpilesinthegroupofpilesthatactasapilegroup.

④Whendetermining the pulling resistance of piles, it is necessary to consider the limit value of the upwarddisplacementofpileheadsbypullingdeterminedbythesuperstructure.

(2)TensileStrengthofPileMaterialsThedesignvalueof thepullingresistanceofpiles is limited to the tensilestrengthof thepilematerials. Themethodofexaminationcanconformto2.4.3[5] Examination of Compressive Stress of Pile Materials.

2.4.5 Static Maximum Lateral Resistance of Piles

[1] General

(1)The staticmaximum lateral resistance of a single pile shall be determined as appropriate on the basis of thebehaviorofthepilewhenitissubjecttolateralforces.

(2)Thecharacteristicvalueofthestaticmaximumlateralresistanceofapilemustbedeterminedsoastosatisfythefollowingtwoconditions:

① Thepilematerialshallnotfailduetostressgeneratedinthepilebody.Especiallythepilematerialshallnotfailduetobendingstressgeneratedinthepilebody.

② Thedisplacement in lateraldirectionand inclinationof thepileheadshallnotexceed the limitvalueof thedisplacementdeterminedbythesuperstructure.

(3)PenetrationLengthofPilesThelengthofpenetratedpartofpilethatyieldseffectiveresistanceagainstexternalforcesiscalledtheeffectivelength.Pilesarecalledlongpileswhenthepenetratedlengthislongerthantheireffectivelength.Pilesarecalled


–457–

shortpileswhenthepenetratedlengthisshorterthantheireffectivelength.

(4)PilesSubjecttoLateralActionsTheresistancewhichapileperformswhensubjectedtoactionsinthelateraldirection(actionsinthehorizontalornear-horizontaldirection)iscalledthelateralresistanceofthepile,andmaybecategorizedinthethreebasicformsshowninFig. 2.4.13.63)

(a) Theresistanceof thepile is limited to the lateraldirection,andresistance in theverticaldirectiondoesnotappear.Thisisthesimplestformoflateralresistanceandisfrequentlycalledthelateralresistanceofapileinthenarrowsense.

(b)Somepartoftheresistanceofthepileiscomposedofaxialresistance.However,becausethesharesoftheloadbornebylateralresistanceandaxialresistancearedeterminedalmostentirelybytheinclinationangleofthepiles,resistancemaybedividedintolateralresistanceandaxialresistanceandexaminedseparately.

(c) Coupledpilesarethoseinwhichtwoormorepileswithdifferingaxialdirectionsarecombined.ThesimplestformofcoupledpilesisshowninFig. 2.4.13. Incoupledpiles,mostoftheactionissupportedbytheaxialresistanceoftherespectivepiles.Therefore,whenthefreelengthofthepilesislong,thelateralresistanceisnormallyignoredandonlytheaxialresistanceisconsideredinestimatingresistance.Withcoupledpiles,itisquitedifficulttocalculatethepileheaddisplacement.Sofar,anumberofmethodshavebeenproposed,64),65)butnonecanyetbecalledadequate (see2.4.5[6] Lateral Bearing Capacity of Coupled Piles). However,becausethedisplacementofcoupledpilesisfarsmallerthanthatofsinglepiles,displacementrarelybecomesaproblem.

12

TT TTL

TA T2

TA2

TL1

TA1

TL TA

(a) When one vertical pile is subject to lateral force

(b) When one batter pile is subject to lateral force

(c) When coupled piles are subject to lateral force

Fig. 2.4.13 Piles Subject to Lateral Force

[2] Estimation of Behavior of Piles

(1)Thebehaviorofasinglepilewhichissubjecttolateralforcecanbeestimatedbyeitherofthefollowingmethodsorbyacombinationthereof.

①Methodsusingloadingtests

② Analyticalmethods

[3] Estimation of Behavior of a Single Pile by Loading Tests

(1)Whenloadingtestsareplannedtoestimatebehaviorofasinglepilesubject to lateralforce, it isnecessary toconsidersufficientlythedifferencesinthepileandloadconditionsbetweenthoseofactualstructuresandloadingtests.

(2)LoadingtestresultsandcharacteristicvalueanddesignvalueoflateralresistanceWhenloadingtestsareconductedunderthesameconditionsasthoseinactualfacilities,thecharacteristicvalue

–458–


ofthestaticmaximumlateralresistancemaybeobtainedfromtheloadingtestresultsbythefollowingmethod. The load-pile head displacement curve in lateral loading tests generally shows a curved form from thebeginningoftheloading.Therefore,withtheexceptionofshortpiles,aclearyieldloadorultimateloadnormallycannotbeobtained. Asexplainedpreviously in [1] General, this isbecauseonlygradual small-scale failureoccursinthegroundwithlongpenetrationlengths,andoverallfailureofthegrounddoesnotoccur.Therefore,theload-pileheaddisplacementcurveisnotusedtoobtaintheyieldloadortheultimateload,buttoconfirmthepileheaddisplacementitself.Inotherwords,thefundamentalconceptoftheperformanceverificationofpilessubjecttolateralforceisdeterminationofthelimitvalueofthedisplacementofthepileheadanddesignsoasnottoexceedthatlimitvalue. Furthermore, the bending stress corresponding to the resistance obtained in this manner must also beconsidered.Hence,itisnecessarytoensurethatfailureassociatedwiththebendingstressofthepilematerial(seePart II, Chapter 11, 2.2 Characteristic Values of Steel)doesnotoccurwhentheexpectedloadacts.Tocalculatetheallowablelateralbearingcapacityofshortpiles,overturningofpilesmustbeconsidered,inadditiontothepileheaddisplacementandbendingstressmentionedalready.Whentheoverturningloadcannotbeascertained,themaximumtestloadmaybeusedinsteadoftheoverturningload.

[4] Estimation of Pile Behavior using Analytical Methods

(1)Whenestimatingbehaviorofasinglepilesubjecttolateralforcebyusinganalyticalmethods,itispreferabletoanalyzethepileasabeamisplacedonanelasticfoundation.

(2)Methodsofanalyticallyestimatingthebehaviorofasinglepilesubjecttolateralforceasabeamisplacedonanelasticfoundation include therelativelysimpleChang’smethodswellas thePHRI(PortandHarborResearchInstitute,nameischangedtoPARI)method.68)

(3)BasicEquationforBeamonElasticFoundationEquation(2.4.34)isthebasicequationforanalyticallyestimatingbehaviorofapileasabeamplacedonanelasticfoundation.

(2.4.34)where

EI : flexuralrigidityofpile(kN･m2) x : depthfromgroundlevel(m) y : displacementofpileatdepthx (m) P : subgradereactionperunitlengthofpileatdepthx (kN/m) p : subgradereactionperunitareaofpileatdepthx (kN/m2) B : pilewidth(m)

AnalyticalmethodsdifferdependingonhowthesubgradereactionPisconsideredin equation(2.4.34).Ifthegroundisconsideredsimplyasalinearelasticbody,Porpisalinearfunctionofdisplacementofpiley.

(2.4.35)or

(2.4.36)where

Es : modulusofelasticityofground(kN/m2) kCH : coefficientoflateralsubgradereaction(kN/m3)

There ismuch discussion concerning the characteristics of themodulus of elasticityEs, but the simplestconceptisthatEs=kCHB=constant,asproposedbyChang.69)Shinohara,Kubo,andHayashiproposed thePHRImethodasananalyticalmethodconsidering thenonlinearelastic behavior of the ground.70), 71) Thismethod can describe the behavior of actual pilesmore accuratelythanothermethods.ThePHRImethodusesequation(2.4.41)todescribetherelationshipbetweenthesubgradereactionandthepiledisplacement.

(2.4.37)where

k :constantoflateralresistanceofground(kN/m3.5orkN/m2.5) m :index1or0


–459–

(4)PHRIMethod

① CharacteristicsofthePHRImethodIn thePHRImethod, theground isclassified into theS typeand theC type. Therelationshipbetween thesubgrade reaction and the pile displacement for each ground is assumedby equation (2.4.38) and (2.4.39),respectively.

(a) S-typeground

(2.4.38)

(b)C-typeground

(2.4.39)where

ks : constantoflateralresistanceinS-typeground(kN/m3.5) kc : constantoflateralresistanceinC-typeground(kN/m2.5)

The identificationofS-typeorC-typegroundand the estimationofks andkc arebasedon the results ofloadingtestsandsoilinvestigation. InthePHRImethod,thenonlinearrelationshipsbetweenp andy areintroducedasgivenbyequations(2.4.38)and(2.4.39)toreflecttheactualstateofsubgradereaction.Therefore,thesolutionsunderindividualconditionswouldremainunattainablewithouthelpofnumericalcalculation,andtheprincipleofsuperpositioncouldnotbeapplied.Theresultsofmanyfull-scaletestshaveconfirmedthatthismethodreflectsthebehaviorofpilesmoreaccuratelythantheconventionalmethods.Itiscommentedherethatforpilestobehaveaslongpiles,theymustbeatleastaslongas1.5 m1( m1:depthofthefirstzeropointofflexuralmomentinthePHRImethod).64)

② ConstantsoflateralresistanceofthegroundThetwogroundtypesinthePHRImethodaredefinedasfollows;

(a) S-typeground

1) Relationshipbetweenp-y isexpressedasp=ksxy0.5 refer(2.4.38)

2) N-valuebythestandardpenetrationtestincreasesinproportiontothedepth.

3) Actualexamples:sandygroundwithuniformdensity,andnormallyconsolidatedcohesivesoilground.

(b)C-typeground

1) Relationshipbetweenp-y isexpressedasp=kcy0.5 refer(2.4.39)

2) N-valuebythestandardpenetrationtestisconstantregardlessofdepth.

3) Actual examples: sandy ground with compacted surface, and heavily-overconsolidated cohesive soilground. ArelationshipshowninFig. 2.4.14existsbetweentherateofincreaseintheN-valuepermeterofdepthinS-typegroundN andthelateralresistanceofpilesks.72)IncaseswherethedistributionoftheN-valueinthedepthdirectiondoesnotbecome0atthegroundsurface, N canbedeterminedfromtheaverage inclinationof theN-valueplotting through thezeropointat thesurface. InC-typeground,arelationshipofthetypeshowninFig. 2.4.15existsbetweentheN-valueitselfandkc.68),73)Thus,aroughestimateofksorkccanbemadefromthedistributionoftheN-value

.

–460–


104

103

102

101 100

11

1412

107

1539

8 2

13

64

1

5

N-value

ks

(kN

/m3.

5 )

1. ALTON.ILLINOIS (FEAGIN)2. WINFIELD.MONTANA (GLESER)3. PORT HUENEME (MASON)4.5. Hakkenbori No.1, No.26. Ibaragigawa (GOTO)7. Osaka National Railways (BEPPU)8.9. Tobata No.6, No.910. Tobata K-I (PHRI)11. Tobata K-II (PHRI)12. Tobata L-II (PHRI)13. Kurihama model experiment14. Shin-Kasai Bridge (TATEISHI)15. Yamanoshita (IGUCHI)

Fig. 2.4.14 Relationship between N-value and ks

1. Tobata K-I (TTRI)2. Tobata K-III (TTRI)3. Tobata K-IV (TTRI)4. Tobata L-II (TTRI)5. Tobata L-IV (TTRI)6. Hakkenbori No.17. Hakkenbori No.28. Osaka National Railways9. Yahata Seitetsu No.610. Yahata Seitetsu No.911. Tobata preliminary test-1 (TTRI)-112. Tobata preliminary test-2 (TTRI)-213. Wagner (Callif.) No.1514. Wagner (Callif.) No.2515. Wagner-1 (Alaska)-116. Wagner-1 (Alaska)-217. Tokyo National Railways b18. Tokyo National Railways A419. Tokyo National Railways B

1

2

3

4

5

67

8

9

9

10 11

12

1314

15

16

1718

103

102

104

1 10 100N-value

kc

(kN

/m2.

5 )

Fig. 2.4.15 Relationship between N-value and kc

③ EstimationoflateralresistanceconstantsbyloadingtestsEstimationsofthelateralresistanceconstantsbyusingtheN-valuecanonlyprovideapproximatevalues.Itispreferabletoconductloadingteststoobtainmoreaccuratevalues.Theconstantsks andkc aredeterminedfromthegroundconditionsalone,andareunaffectedbyotherconditionsunlikeEs inChang’sequation.Therefore,ifks orkc canbeobtainedbyaloadingtest,thosevaluescanbeappliedtootherconditionsaswell.

④ Effectivelength Foracertainpiletofunctionasalongpile,itspenetrationlengthmustbegreaterthanitseffectivelength.Basedontheresultsofmodeltestswithshortpiles,ShinoharaandKubofoundthat thelowerpartofapileisconsideredtobefixedcompletelyinthegroundwhenthepenetrationlengthexceeds1.5 m1,andthereforeproposedusing1.5 m1aseffectivelength.77)Actually,ifthepenetrationlengthexceeds1.5 m1,thebehaviorofthepilewillnotdiffersubstantiallyfromthatofalongpile.However,astheminimumpenetrationlengthoflong


–461–

piles,1.5 m1shouldbeused,consideringtheeffectsofsoilfatigueorcreep. Itshouldalsobenotedthatthevalueof m1increasesasthestiffnessofthepileincreasesanddecreasesasthelateralresistanceofthegroundincreases.However,thevalueof m1isvirtuallyunaffectedbytheloadingheightandpileheadfixingconditions. Furthermore, m1alsohas thecharacterof increasinggradually as loadingincreases.

⑤ EffectofpilewidthTherearetwowaysinconsideringtheeffectofpilewidth.ThefirstistoconsiderthatthepilewidthB hasnoeffectontherelationshipbetweenthesubgradereactionp perunitareaandthedisplacementy.Thesecond,asproposedbyTerzaghi,istoassumethatthevalueofp correspondingtoagiveny valueisinverselyproportionaltoB.Shinohara,Kubo78)andSawaguchi79)conductedmodelexperimentsontherelationshipbetweentheks valueinsandygroundandB.TheresultsareshowninFig. 2.4.16.ItseemstoshowacombinationofthetwotheoriesmentionedaboveandindicatesthatthefirsttheoryiseffectiveifthepilewidthB issufficientlylarge.Onthebasisoftheseresults,itwasdecidednottoconsidertheeffectofpilewidthinthePHRImethod.

+

Pile width (cm)

Late

ral r

esis

tanc

e co

nsta

nt ks (

kN/m

3.5 )

12

10

8

6

4

2

00

10

20 30 40 50 60

×103

Legend

Pile headdisplacement p-y curve

Maximumbendingmoment

1st Series2nd Series3rd Series

Fig. 2.4.16 Relationship between ks and Pile Width

⑥ EffectofpileinclinationForbatterpiles,arelationshipshowninFig 2.4.17existsbetweentheinclinationangleofthepilesandtheratioofthelateralresistanceconstantofbatterpilestothatofverticalpiles80)Thistigureshowsthein-situtestsexampleswhichexamineddrivingofbatterpilesinhorizontalgroundandthelaboratorytestsexamplesobtainedbypreparingthegroundafterdrivingofthebatterpileandthensufficientlycompactingthegroundaroundthepile.Inthein-situtests,whenfillingwasperformedafterthebatterpilesweredriven,resultswereobtainedinwhichthecoefficientofthesubgradereactiondidnotincreaseevenwhentheangleofinclinationof thepile isminus. In thiscase,however, an increase in thecoefficientof the subgrade reactiondue tosubsequentcompactionofthesurroundinggroundcanbeexpected.81),82)

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0-30 -20 -10 10 20 30

2.5

2.0

1.5

1.0

0.5

:Indoor tests:In-situ tests

k0：　

x=k/k 0

(in) (out)

θ

Value of k, when θ = 0

-θ +θ

Fig. 2.4.17 Relationship between Pile Inclination Angle and Lateral Resistance Constants

(5)Chang’sMethod

① CalculationEquationUsingtheelasticitymodulusofthegroundEs =B kCH,theelasticityequationofpilesisexpressedasfollows;

Exposedsection

(2.4.40)Embeddedsection

BycalculatingthesegeneralsolutionswithB kCH asaconstantandinputtingtheboundaryconditions,thesolutionforpilesofsemi-infinitelengthcanbeobtained(seeTable 2.4.6).83) AccordingtoYokoyama,pilesoffinite lengthmaybeequivalent to thepilesof infinite lengthifβL ≥ π .Whenapileisshorterthanthis,apilemustbetreatedasafinitelengthpile.Diagramsareavailabletosimplifythisprocess.85)


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Tabl

e 2.

4.6

Cal

cula

tions

for P

iles

of S

emi-I

nfini

te L

engt

h if

k ch

is C

onst

ant

Differentialequationsofdeflection

curveandexplanationofsy

mbols

Exposedsections:

[Sym

bols]

Embeddedsections:

Ht :Lateralforceonpilehead(kN

)M

t :Externalforcemom

entonpile

head

(kN

･m)

B :Pilediameter

(m)

EI :Flexuralrigidity

(kN

･m2 )

k CH

:Coefficientofhorizontalsubgradereaction(kN

/m3 )

h :Heightofpileheadaboveground

(m)

β :

(m–1

)

Situationofpile

Protrudingaboveground(h≠0)

Embeddedunderground

(h=0

)Deflectioncurvediagram

Flexuralmom

entdiagram

①Basicform

ation

②Ifpileheaddoesnotrotate

③Basicsy

stem

(butM

t=0)

④Ifpileheaddoesnotrotate

Deflectioncurvey

(IfM

t≠0,useequationsin①

putting

h0=M

t/Ht:thesameappliesb

elow

)Pileheaddisplacement

y t

Groundleveldisplacem

ent

y 0

Pileheadinclinationθ

t

Flexuralmom

entofpilemem

bersM

Shearstrengthofpilemem

bers

S

Pileheadflexuralm

oment

Maximum

flexuralmom

entof

embeddedpartsM

s,max

Depthatw

hich

Ms,m

axoccurs m

Depthof1ststeadypoint0

Depthofdeflectionanglezeropoint

L Pileheadrig

idityfactor

K 1,K

2,K3,K

4

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② EstimationofkCH inChang’smethod

(a) Terzaghi’sproposal86)Terzaghiproposedthefollowingvaluesforthecoefficientoflateralsubgradereactionincohesiveorsandysoil:

1) Incaseofcohesivesoil

(2.4.41)where

kCH :coefficientoflateralsubgradereaction(kN/m3) B :pilewidth(m) :valueshowninTable 2.4.7

(2.4.42)

2) Incaseofsandysoil

(2.4.43)where

x :depth(m) B :pilewidth(m) nh :valuelistedinTable 2.4.8

(2.4.44)

Insandysoil,Es isafunctionofdepthandthuscannotbeapplieddirectlytoChang’smethod.Forsuchcases,ChangstatesthatEs canbetakenthevalueatthedepthofonethirdofy1whichisthedepthofthefirstzero-displacementpoint.However,y1itselfisafunctionofEs,thusrepeatedcalculationshavetobemadetoobtainthevalueofEs.Reference87)describesthemethodofcalculationwithouttherepetitioncalculation. Terzaghi assumes that the value of kCH is inversely proportional to the pilewidthB, as shown inequations(2.4.43)and(2.4.44).OtheropinionssuggestthatpilewidthisirrelevanttokCH(see(4)⑤).

Table 2.4.7 Coefficient of Lateral Subgrade Reaction

Consistencyofcohesivesoil Hard Veryhard SolidUnconfinedcompressivestrengthqu (kN/m2) 100–200 200–400 400orgreaterRangeofkCH1(kN/m2) 16,000–32,000 32,000–64,000 64,000orgreaterProposedvalueofkCH1(kN/m3) 24,000 48,000 96,000

Table 2.4.8 Value of nh

Relativedensityofsand Loose Medium Densenh fordryorwetsand(kN/m3) 2,200 6,600 17,600nh forsubmergedsand(kN/m3) 1,300 4,400 10,800

(b)Yokoyama’sproposalYokoyamacollectedtheresultsoflateralloadingtestsonsteelpilesconductedinJapanandperformedreversecalculationsforkCH, andobtainedFig. 2.4.18 bycomparingtheresultsandthemeanN-valuesatdepthsdowntoβ-1fromthegroundlevel.88)Inthiscase,Es = kCHB isassumedtobevalidforbothsandysoilandcohesivesoil,andkCH itselfisassumednottobeaffectedbyB.AlthoughthevaluesofkCH obtainedbyreversecalculationfromthemeasuredvaluesdecreaseasloadingincreases,Fig. 2.4.18 ispreparedusingkCHwhenthegroundsurfacedisplacementis1cm.Fig. 2.4.18 maybeusedwhenmakingroughestimatesofthevalueofEs fromsoilconditionsalonewithoutconductingloadingtestsin-situ.


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1. Yamaborigawa2. Tobata3. Tobata K-I4. Tobata L-II5. Tobata K-II6. Tobata K-III7. Tobata L-IV8. Tobata K-IV9. Shell Ogishima10. Ibaragigawa11. Takagawa12. Tokyo SupplyWarehouse13. Kasai Bridge14. Aoyama15. Den-en

4

1

2

3

5

6 7

8

9

10

11

12

13

14

15

1 10 50103

104

105

N-value

k CH

(kN

/m3 )

Fig. 2.4.18 Values of kCH obtained by Reverse Calculation from Horizontal Loading Tests on Piles

(c) Relationshipbetweenkc,ks,andkCH 89),90)

FromFig. 2.4.14,Fig. 2.4.15,andFig. 2.4.18,therelationshipsbetweentheSPT-N-valuesorN -valuesshownintherespectivefiguresandthecorrespondingcoefficientsofsubgradereactionareasshowninTable 2.4.9.Ascanbeunderstoodfromtheseresults,therearelargelydispersedrelationshipsbetweenkCHandtheN-value.TheseresultsareduetothefactthatthevalueofkCHcannotbedeterminedfromthesoilconditionsalone. Hence,therelationshipbetweenkcandkCHandthatbetweenks andkCHcanbeobtainedinsuchawaythatgroundsurfacedisplacementwasequalunderthesameloadingconditions.Then,substitutingtherelationalequationsofkc,ks,andtheN-valueorN -value,thefollowingequationscanbeobtained.

(freepilehead)

(fixedpilehead) (2.4.45)

(freepilehead)

(fixedpilehead)

Table 2.4.9 Relationships between SPT-N-value or N -value and Respective of Subgrade Reaction

Correlationequation Correlationcoefficient Coefficientofvariation

(kN/m2.5) 0.872 0.111

(kN/m3.5) 0.966 0.077

(kN/m3) 0.917 0.754

TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND … · TECHNICAL STANDARDS AND COMMENTARIES FOR PORT AND HARBOUR FACILITIES IN JAPAN The design values in the equation may be calculated

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